Each community enforces its norms, including the principle "search first, post later"; Stack Overflow, Inc.'s terms and conditions and code of conduct might also be enforced by staff. The site community starts with default content for elements like the tour and helpful articles. During the beta, the community should agree on how to set some elements.
Please note that the site's tour pages, as we see them nowadays, were launched in January 2013. Many sites were launched before; among them are Stack Overflow and Philosophy.
By the way, this might look like a duplicate of a very old post from 2009: Can (and should) more be done to encourage users to search first and ask only if they don't find an existing answer?. I will not think that this should be closed as duplicate as that post is very old, and many things have changed since then, especially the company leadership, its relationship with the community and the many users that used to be active those days are no longer active due to company changes and for many other reasons.
Stack Overflow and Phylosophy were created before the tour page design was launched in January 2013, but they are sites in very different circumstances.
Stack Overflow is the flagship of the public Q&A platform and the main "victim" of the company. It was launched in 2008 and is near to celebrate its 15th anniversary. The first post was created in July 2008. Currently, it's deleted, but it could be seen by users having +10k rep and probably in other places. Stack Overflow has several features that aren't available on other sites.
Philosophy first post was created in 2011. It is a relatively small community focused on a non-technology topic, so the workings of this site might be very different than those of Stack Overflow.
"search first, ask later" historical purpose is avoiding having the same question repeatedly. This is more relevant on sites having a large activity and phenomena like "eternal September", as happens on Stack Overflow, people new to programming go directly to ask a question instead of studying, searching, etc.
There are variations of this principle as well as other related ones like "read the fine manual", "rubber duck", "general questions", and "challenging questions".
Ideally, each community should clearly state what kind of questions they want instead of keeping boilerplate texts like (taken from the Super User tour)
With your help, we're working together to build a library of detailed answers to every question about computer software or hardware.
Many tour pages only changed "computer software or hardware", but they could change the wording of the whole statement. They could change the whole tour introduction.
Get answers to practical, detailed questions
Focus on questions about an actual problem you have faced. Include details about what you have tried and exactly what you are trying to do.
The Ask Question has several guidance elements having boilerplate text. Those elements can be customized according to each community's needs, i.e, resulting from the transposition of the Q&A model to the community topic and scope and needs.
As someone having just one month participating in SO / SE, I suggest you focus on one community to learn its workings and avoid confusion about them. While some might have a group of users participating on multiple sites, and some have community moderators being community moderators on multiple sites, each community is independent of other communities.
Regarding https://stackechange.com, it might help to do global searches but be aware of several known issues.
- Don't have high expectations about known issues being fixed quickly or "fun features" to be updated soon:
- The company changed its name from Stack Exchange, Inc. to Stack Overflow, Inc.
- With the new name and corporate image redesign, among other stuff, new sites and initiatives are being prioritized over the features and content of https://stackexchange.com.
Before making a feature-request, test the waters in the community in focus
- You have been very lucky to get your first post on Meta Stack Exchange, so well received (31 upvotes). This is rarely seen on feature-request from new contributors. By the way, well deserved as you have shown have researched and thought deeply about the question. Congratulations.
- Be aware that some communities are not interested in updating the site tour besides questions and answers, i.e., tag wikis.
- Some communities do not have daily or weekly activities. Some might not have new posts for several months, some new questions might not get any reaction in several days or even months. I mention this because it looks like the Community Management team will not support / invest in any noncritical feature-request that doesn't have a clear backup of the community. It's not clear what is the minimum required. I assume that it's determined case by case and be circumstantial.
Once you have a clear idea of proposing a change in the community in focus and know it might be well received, post a feature-request.
You might be bold and go directly to posting a feature-request. Probably you have the skills and luck to have a status-completed on your first attempt. Getting a few badly received posts is not bad at all but having many might grant you a post ban (ref. What can I do when getting "We are no longer accepting questions/answers from this account"?).
As I mentioned in a comment, the question looks too broad.
Also, the title is not summarizing the question body properly; the body mix element of different nature; some are about the workings, other about using the platform.
I found it unfortunate that someone added feature-request during the moderation strike.
Comments about the presumptions / Impressions
A -> This corresponds to one of the premises of Q&A model.
B -> Some communities allow unregistered users to post questions and answers, but on some sites, being willing to ask a question is a "great motivation" to become a registered user / create an account, as it's the only way to do so. In other communities, the motivation to become a registered user might come later, sometimes forced when the user uses different devices, among other technical reasons.
- You got it correctly; communities have limited autonomy. Each community has its pro-tempore / community moderators, with very few exceptions each community has its own Meta.
- Tour. The current tour is an evolution of the FAQ / About page used on the old communities. The tour was launched in January 2013. Nowadays, pro-tempore / community moderators can customize tour elements.
- Stack Exchange, https://stackexchange.com/tour and Meta Stack Exchange, https://meta.stackexchange.com/tour have unique "tour". The first is because it's not a community tour but a network one. Meta Stack Exchange tour is also different as its topic is the network, so several things work differently than on the communities.
- Per-site-metas don't have a tour page.
- Ask Question page
- Stack Overflow is the flagship; it's the site with the largest activity. It has several unique features.
D -> The search box on each community scope is only the corresponding community. Users interested in using Stack Exchange features to search the network instead of using Google or another third-party search engine might use "global search" from https://stackexchange.com. The "global search" and other https://stackexchange.com features have known issues.
Could or should the "search first, ask question later" principle be made more prominently visible?
This is primarily opinion based. On discussion in Meta Stack Exchange, this is perfectly fine. The problem is that this title might make readers think that question is about making a site design change request, tagged here with feature-request, while it looks embraces other things. A signal that the question is too broad is ending it with a list of questions.
Let's jump directly to the questions at the end of the question body.
- Is the "search first, ask question later" principle indeed as established network-wide as my impression suggests?
As I mentioned in a comment, this is part of the Q&A model. It might or might not be enforced by each community. Theoretically, this is defined during the site proposal and the site beta. This might be reviewed and changed on "graduated sites".
- Could there be any improvement, say on the tour-pages, so that new users who join to ask a question (and others) can get a clearer understanding of what exactly the search-first expectation is, so they're neither totally discouraged to ask nor find out pretty late that they did something wrong?
Yes. Once you have a specific proposal and know it will be well received, post it using feature-request on the corresponding per-site-meta if it's specific to one community or here if it's something that might benefit / affects all sites and requires important budget (staff, time, ...).
Note: A change to a tour page might imply a change to the community norms (rules, policies, practices...). The community moderators might make some changes, like changing the tour introduction content. Making a trivial change might not require a feature-request, but doing a change that might be perceived by an important number of active community members as a policy change, should be supported by a feature-request.
- Can this even be answered in general or is this a topic that each community discusses and decides for itself?
The Q&A model and the platform that supports it should be optimized for putting into practice the "search first, ask later" principle and the "lower barrier entry possible" principle, among others.
"Lower barrier of entry" means trusting that most new users have the minimal knowledge and skills required to ask and answer questions on the corresponding community according to its topic, scope, workings, terms and service conditions and code of conduct.
Users might be aware or not of and might see or not the "search first, ask later" principle as a hard rule. Their stand about this principle might be circumstantial, i.e., on a site having low activity, having a new question might give them such happiness that they won't be interested in enforcing it.
Come to Meta Stack Exchange (Meta SE) when you want to ask for a site recommendation when you find a bug that might affect multiple communities. Also, you might come to Meta SE to propose a feature request that might benefit multiple communities or affect them.
You can come to Meta SE to learn from site recommendations and bugs posted by others. You might also come to Meta SE to learn about the Stack Overflow and Stack Exchange network history and their users collaborating on multiple sites, to ask about common topics like using Stack Exchange Data Explorer and the current moderation strike.
I recommend people new to SO/SE stick to one community for a while until they learn the workings of such a community. Those being lucky will find an active community. Those unlucky might be stuck, unable to earn the reputation needed to get the privileges required to extend their participation.
If people can't stick to one community, if the community initially chosen hasn't more active users or with very slow activity because they are eager to collaborate on stuff that is split across multiple sites, i.e., spreadsheets, then they should prepare themselves to have deal with multiple norm enforcement practices and with sites having different features and customization levels.
While the Q&A model and platform supporting SO / SE is "one", each site is "run" by "each user", collectively referred to as "the community".
Each user uses the Q&A platform model in its way. Some users have agreed with other users to use certain features in a certain way and have agreed to use certain vocabulary; some call these agreements "community consensus". Some users feel that they belong to a community, and make others feel belonging to a community and are welcoming. Some users are just jumping from one site to another, using each site their way. When getting "feedback" try to identify if it comes from someone talking on behalf of the community or if they are talking on behalf of themself. Don't rely just on the words selected; look that their feedback matches the community spirit.