Hello,
When I join a table, sounds don't start playing until I click table actions.

i remember it being like that. for now you just have to do it that way. i'm guessing it is an unseen bug or something

Hello,

This is infortunately a well known limitation of iOS, that can be left only if I make a native app available on the appstore.
Perhaps a day I will do it, but for now you have to bear with this little annoying behavior.

The limitation is mainly there for political rather than technical reasons. Apple wants to favor apps on the appstore against applications that can be directly accessed on the web like the playroom is, and they do it by putting some small annoying limitations like this one.