Finding the right space for a community is a difficult process and creating a SE site is difficult for its own reasons. Your research may have uncovered these already but I'm going to try cover everything I can think of rather than leave things out you may already know but others may not.
Creating a niche community on SE
It wouldn't be totally impossible to create a niche community like the one you've described here on SE - but it could be difficult. There are a handful of questions that I'd want to be able to answer before I started a new site proposal on Area 51 to assess whether SE is a good fit and whether there's an interest the change.
There are likely others, but this is what came to mind after reading the question:
- How many of the existing community members currently use SE and have some reputation?
The Area 51 process gives communities a short window of time to muster support through its early phases, which includes needing commitments from existing SE users who have earned some reputation on existing SE sites. This is generally easier in tech industry related subjects due to there being so many tech people on the network already. This reputation must be earned legitimately and naturally. While rare, staff have discovered cases in the past where communities have coordinated efforts to falsely push the site through the definition and commitment phases, which can lead the proposal to be shut down or, in extreme cases, banned outright.
- How many truly active and engaged members are in your community who would be interested in moving to another platform?
When answering this question, you should think critically about many things - for example, the answer to the prior question. If no one's heard about SE but they all use your current platform regularly, are they going to want to migrate elsewhere? It's also worth considering whether SE site scope (see answers to 3 below) only meets the needs of part of your current platform's use case. Particularly if the admins of the existing community aren't interested in prohibiting the SE-appropriate content on the current platform, you may end up dividing the community and may lose some of the experts who are unwilling to move here.
- What sorts of questions are being asked? - not all sorts of questions are a good fit for the SE model and understanding what sorts of questions the community has will help determine if SE is a good fit.
- Do such questions generally have objectively correct answers or do they lean towards discussion-type conversations?
SE sites should focus on questions that have objectively correct answers or are subjective but follow the "Good Subjective" practice that expects evidence- or experience-based answers. If most questions are very subjective or lead to long discussion rather than concise solutions, the community's needs may not fit well into the SE format.
- Are the answers to questions broadly applicable to most people and reusable?
One of the core concepts of SE sites is as a resource that has reusability. While sites do see questions that are very specific to one person or situation, these should not be the bulk of questions on the site. While sites (e.g. Law) often see questions that may only relate to a specific region or culture, the answer should be generally be applicable for people in that group.
- Will answers to questions remain a useful resource long-term?
One issue with most documentation formats is when the content stales and no longer reflects current knowledge. This leads to the resource being outdated and if people don't continue to curate and improve it, people may stop using the resource. While things change over time, the more frequently they change, the greater risk that the content on an SE site will age or require more effort from curators to keep updated.
- Are questions on topic elsewhere on the network?
While I understand that people may feel more comfortable going to a place just for them, that's not really how the SE Network is designed to work. People have questioned this and there has certainly been a movement towards considering smaller communities successful, it's difficult for me to imagine SE going in the direction of Reddit, where subs are easy to create and there are thousands of them. If most questions are in scope for another site, it's unlikely that the company will allow the proposal to proceed far in the Area 51 process.
- Can questions be open and public to the broader internet with no membership requirements?
This actually isn't a question I would normally have thought about but it comes to mind specifically when thinking about medical issues. Many platforms allow admins/mods to control access to a group/sub/channel, etc. - that's not possible on Stack Exchange. All public sites are public - to everyone, even without an account. Communities that need to restrict access to site content probably shouldn't consider SE as a good fit for their content.
If you feel like your community can be well-served and successful considering your answers to these questions, then go ahead and propose the site on Area 51 but understand that it generally takes several months to complete the process, depending on how engaged and interested your community is in joining this new space.
More on scope overlap with other SE sites
Since I'm guessing the focus of your query relates primarily to point 4 above, I'll say that I understand your concerns about finding a space that truly feels like home for a niche community and questioning whether that's something Stack Exchange will permit. As I've already said, at this point, I'm guessing it's not. With the current platform design, it's simply too difficult for the company to launch new Stack Exchange sites and the risk of siphoning good content from existing, broader sites is high, even if a proposed site's questions haven't previously been asked there.
I've discussed this previously in an answer to this related question - How can I more easily access all content related to a specific subject? - which is more about a potential site's content being spread across many sites but my answer is pretty relevant here, too.
It's very common for people to want - or at least be used to - extremely segmented communities deeply focused on one specific subject. That could be a Discord community focused on a favorite game or a forum with experts about their profession or a Facebook group like the one you mention. While any person may not participate in every aspect of such a community, everything in that community is about that subject.
Stack Exchange was never built to be that - with Stack Overflow as its model, sites were created to cover very broad subjects, though very niche sites did manage to find their way to launch even early on - e.g. Chess in 2012. In general sites have covered far more than the communities you might see on Fandom or in a forum - instead of separate sites for Star Trek and Star Wars, they share a site with the rest of Sci-Fi - and Fantasy, too.
This model has value for curation and moderation but likely discourages people from participating who don't feel the community is interested in the same thing they are, as in your case and your dismissal of Medical Sciences. Despite my experience on SE, I've personally joined Discord channels or used Reddit to find answers about the video games I play rather than asking questions on Arqade because of this. There may be some games I'd ask about there but since I never see questions about the games I play, I go elsewhere.
Unfortunately, this leads to SE sites being less active and containing less content than they might otherwise and has a snowball effect... when I don't ask questions about the games I play, others won't see that game represented on Arqade (and search engine results won't refer people there) and may feel like the experts in that game are elsewhere and find a niche community instead. That said, the questions I have asked on Reddit or Discord usually fail one or more of the three tests mentioned in bullet 3 above, so the game being in-scope but having no apparent experts on Arqade might not really be the core issue.
Finding a space on an existing site
While I understand your concerns about wanting a space just for your subject, if your answers to the questions above still indicate that SE is a good fit other than scope overlap with an existing site, please do consider joining an existing site rather than going elsewhere. The best way to combat the snowball effect is for people to make a space for themselves on an existing site and show the others in their community that they're welcome, even if the scope is broader than you'd prefer.
If you're concerned about whether questions would be accepted on an existing site, check the site's on topic help page (/help/on-topic) to see if there's any information and then visit to their child meta and ask. Share some recent example questions you think meet the expectations of the sort of questions the site allows and see if the community has concerns or would welcome you openly.
Then, work with members of your current space to encourage them to come to the SE site, explain what sorts of questions can be asked and how much more value could be had if they used a purpose-built Q&A space rather than Facebook.
Conclusions
I've spent 8 years poking at SE and understanding how it works - while I can't say I know it best, I know it better than most, so I hope my explanation has given you something to think about. SE is an excellent platform for communities who really just want focused Q&A with some chat spaces attached but it's not a great fit for every community.
In some ways, I think the Area 51 focus on expecting new site proposals to attach an existing community that wants a space for Q&A to the proposal directly conflicts with the traditionally-broad scope of sites, since most existing communities don't want to expand beyond their current subject but are likely as narrow as your Facebook Group's scope.
Without core changes to the platform to allow for community administration of controls that currently require staff, it's unlikely that SE sites will ever proliferate in the way that other platforms have and, as such, niche communities interested in SE-style Q&A - particularly those that overlap existing sites' scope are more likely to find a space on the network by joining an existing site than creating a new one of their own.
