If they're banned from their own instance, that ban federates out and they're completely banned off that account.
If some other instance bans them, that ban is instance specific and that person can still interact with communities and people from other instances, except the one that banned them.
There were some motherboards that had something of that nature (Asus had ExpressGate IIRC) but they were all hilariously incomplete because they didn't realize how useful as a diagnostic thing it'd end up being and tried to sell it off as a "quick boot" thing.
(on the off chance anyone here's using a client that does not show it, i am not from Beehaw and just federating from the outside, just for some context, and it's almost 5AM so expect some half-sleepy rambling)
Honestly something along these lines might just be what the Threadiverse needs. I believe the current threadiverse "culture" is really just a carbon copy of Reddit, with all the downsides, and facing same eventual fate as any other Reddit alternative that came before it.
Mastodon is in it's current state (and it's definitely not without it's own problems by the way) due to the existing culture it had before any of the Twitter migrations it endured. The people that vibed with that culture stuck, the ones that didn't went elsewhere.
If, after a few years of refinement on the threadiverse side (perhaps with actually usable software being built since then) Beehaw suddenly decides to enter back into the picture with a sold userbase and a high quality culture of it's own (and an AP compatible forum software that has proper moderation tooling), it's norms might take over a substantial part of whatever's left of the existing Lemmy community (I'd bet it's gonna be not much more than the stubborn FOSSbros), and any future migrations since then will result in people who don't vibe with that culture skipping over the 'verse (perhaps because they want a freeze-peach platform they can spout whatever they want on), and only the people who can adapt will self-select in.
I always expected a split to happen in the 'verse between the Reddit-style free-for-all folk and the strict moderation folk, but my prediction always assumed that the tools would get built by this point. Considering that doesn't seem to be happening any time soon, this is the next best thing I can hope for. Well, that or the threadiverse fades into obscurity as a failed experiment (hey, remember prismo? me neither) and as something to look at for future AP implementers on what not to do, with most of it's userbase either moving to other platforms or towards other fedi implementations that adopt groups (I believe both Pixelfed and Mastodon are working on them, and the *keys already have Channels (though those don't federate and are local only))
The thing I'm trying to say is that "having an API" does not matter in the long term if the API does not expose the functionality needed to use it properly.
And TBF if someone joined Lemmy only because it had an API and nothing else then they're gonna be in for a very rude awakening sooner or later as the troubles of federation that previous (mostly microblogging) platforms have encountered and attempted to solve (not to mention novel problems due to the community oriented nature of Lemmy) start to show up.
This is only going to get worse, and throwing "more API" into the fire won't fix any of the important problems at hand.
CRONCHY