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UnrealIRCD front-ended by TheLounge web interface that has history would fit what you described, but the setup is not super quick. No registration would be required, TheLounge provides chat persistence. Both are open source. Visitors would not need to be technical and would not need to know IRC commands. Rooms can be deleted by the channel operator. TheLounge is browser based and does not require any additional software.
[1] - https://www.unrealircd.org/ https://github.com/unrealircd/unrealircd/
[2] - https://thelounge.chat/ https://github.com/thelounge
UnrealIRCD front-ended by TheLounge web interface that has history would fit what you described, but the setup is not super quick. No registration would be required, TheLounge provides chat persistence. Both are open source. Visitors would not need to be technical and would not need to know IRC commands. Rooms can be deleted by the channel operator. TheLounge is browser based and does not require any additional software.
[1] - https://www.unrealircd.org/ https://github.com/unrealircd/unrealircd/
[2] - https://thelounge.chat/ https://github.com/thelounge
> No registration needed for group members
This one is the most troublesome I think.
Usually this is in a conferencing solutions though, so no such thing as chat rooms, I think.
Otherwise I would suppose something like XMPP with a web frontend, eg https://movim.eu/
ejabberd supports anonymous users, though I can't say if movim or any else web-client supports that natively
https://www.ejabberd.im/Anonymous-users-support/index.html