which makes it very clear that the only reason PWA where still allowed by apple was to try to avoid monopoly marked regulations

the fact that they seem to remove them without any warning make it clear how much they care about they users (i.e. not at all, it's all about money, which should be obvious but needs to be said in case of apple as they managed to convince people otherwise)

Yes, Movim and Converse.js are two web-based XMPP apps that support installation as a PWA.

XMPP supports running over websockets (or even long-polling HTTP, but that's thankfully less necessary these days).

For servers that enabled web sockets that's possible and XMPP JavaScript libraries support that.