Containers has this weird problem where it's impossible to delete them once you FF sync them.... you will always get new copies of very old containers over and over again. It's a giant mess. So I got discouraged from using them. Every year or 2 I have another look to see if anyone has solved the problem without having to make a new FF sync account which I don't want to do. Maybe I will have another look at the state of things because I have been wishing to have this ability recently with the threadiverse. Just warning you: do not sync the containers! You will regret it.
Mobile is sort of easier because you can repeatedly "install" the PWAs and they seem to have separate sessions. It's not as slick as using one of the reddit clients that allowed changing identities on a per-comment basis but also not bad. I guess they are using some sort of containers implementation which is hidden from the user. If I would get around to jumping through the hoops to install addons on FF mobile, I wonder if your addon would work and if the configurations would also be uniquely stored in the PWA sessions. I've hardly used addon in mobile. If it did function that way, it'd be like >60% of the way to a kbin client. Which doesn't otherwise exist AFAIK, but I could have missed something. And a lemmy client of course.
If it was possible to direct a "share" in android to a specific PWA it might be a close enough to switching per-comment. You could share the location to the other PWA and pick it up from there. But that sounds like something that wouldn't be allowed. If it would even be theoretically possible. About which I have no idea.
What is Connect? I have KDE Connect and there is something called Mozilla Connect but I guess you are referring to something different.