Earlier quoted context omitted.
Have the room owner create an AES 256 key, send it to all Party members via 1:1 e2ee, encrypt room messages with that AES key.
this is pretty much what Matrix does, if I understand correctly. Additionally the key is regularly updated to provide some degree of perfect forward secrecy and avoid encrypting for people who left the group chat
I think it has senders encrypt messages with each room member's public key, rather than a single shared key. (At least, that's what the behavior I've seen suggests to me.)
Here's the spec, in case you want to comb through it:
https://spec.matrix.org/v1.11/client-server-api/#end-to-end-...