On Matrix, as long as you have your username and password, it’s not possible to get “locked out” due to not having your keys. In fact, your keys are only necessary if you plan to participate in encrypted chats, in which case it’s obvious that losing your key will mean losing access to old messages. However, you will still be able to receive new messages by generating a new key.

I use MediaMTX. You can stream to it with whatever (I use OBS). You could even publish it to a website behind an iframe.