So long as you aren't relying on Facebook to log you into other sites, it's pretty seamless, and any edges (including that one) are consequences of the containerisation itself, they're evidence it's protecting you. For example, I pay for Youtube, so I don't see adverts, but inside the Facebook container Youtube has no idea that's me, so any Youtube videos embedded in Facebook have ads like for other users. If I leave Facebook and play the same video outside, no adverts.
Multi-account containers aren't curated (well, you do the curating) so for non-trivial sites (where they'd be most useful) you can expect to spend time tweaking things to ensure that e.g. MyBank-savings.example is inside the same container as MyBank-account.example and NewBrandFor-MyBank.example as otherwise confusing stuff can happen as the containers isolate things you actually wanted connected.
[0]:https://addons.mozilla.org/en-US/firefox/addon/multi-account...