I know that the Community user is in every site, but when looking at its profile on any individual site, it says "This user does not participate in any other communities currently":
Why is this?
I know that the Community user is in every site
I would like to challenge this premise. I would instead phrase it as:
I know that a Community user is in every site
That is to say that while there is a Community user for each site, why would you think that they are the same user? There is also a user Alex on every site (probably, I haven't actually checked) but they are not necessarily the same user. Their sites do not show up in each other's profiles just because they have the same name.
That particular list is generated based on cached information from the network account that ties all of your per-site profiles together. But the Community user doesn't have such a network account. It's literally just a series of profiles assigned to ID -1 that exist on each site, but they are not tied together in any way at the network level outside of being mapped to a non-existent network account (ID -1 as usual). So while the profile does exist on every site, there's no network information that maps them all back to each other, and thus there is no cached list of profiles to display in that space.
Note that this behavior is different for Area 51 and the API, which do not rely on the user map at the network level but rather just query for all sites where there is a user with a matching AccountId set. This method is not dependent on an actual network account existing.
Contrary to what it looks like, all Community’s accounts are linked. The easiest way to see this is Area51:
You can also see this via the app, which means it’s exposed via the API.
This is very similar to the profiles being hidden, but there’s differences like a link to the Stack Exchange profile and a message under “Communities” instead of a link to the one profile. Therefore, it looks like it’s something made to emulate hidden communities.
It actually makes a lot of sense if you think about it. Community ♦ represents the community of a site, and each site has its own community. If SFF.SE's Community ♦ also had an account at Stack Overflow, that would be equivalent to saying that SFF.SE's community is identical to that of Stack Overflow's, which is absurd.