These are completely orthogonal things.

• XMPP is a protocol, just like HTTP or WebSocket
• ejabberd is an implementation of server for such protocol in Erlang. Just like Cowboy is an implementation of server for HTTP/WebSockets.
• Phoenix.PubSub is an helper library for exchanging messages between Erlang nodes.

It is not comparable at all.

No, Phoenix.PubSub do not use WS, it do not use Phoenix at all. It is my biggest gripe with that library, that there is phoenix in its name. It is completely independent from any web or Phoenix technology. It uses defined transport (by default pg which uses Distributed Erlang), but it can use any other messaging technology out there.

These also are orthogonal. WebSocket is more like transport protocol (like TCP, but a little bit higher level as it utilises TCP underneath) and XMPP is data protocol (more like HTTP).

Technically - yes, but it would be IMHO a little bit pointless, as it would introduce a lot of overhead with encoding and decoding all that XMLs. So instead it would be better to use for example Kafka or PostgreSQL LISTEN/NOTIFY.

I will read more about protocols.

Thank you so much for clarifications.

I sense some X/Y problem here. It would probably be better if you state what objective you want to achieve first, so other people can make recommendations for you to choose from.

Ejabberd or XMPP in general is meant for an industrial strength chat application with a rich and extensible set of functionalities, on a federated network governed by multiple entities. You may or may not need that.

Using Phoenix Liveview one put together a simple chat application quickly. I have one too:

I do not even use PubSub/Presence. There is more than one way to do it