For the nostr chat add zap.stream/chat/YOURNPUB to a new web source overlay or as custom OBS widget. Using your npub over eventID will always shows your current chat, no need to update each time you go live. If you want to combine multiple chats, take a look at:

GitHub

GitHub - steveseguin/social_stream: Consolidate your live social messaging streams and much more

Consolidate your live social messaging streams and much more - steveseguin/social_stream