Elixir is interesting for the resilience of BEAM and being FP oriented, and LiveView is a neat concept for templating HTML, but if you are already building a react/typescript front end you wouldn’t get much use out of LiveView. My concern would be issues finding developers to work with that stack and lack of tooling and support outside core libraries.
C# has a very mature product called SignalR that can be used for real time communications with fallback to long polling / SSE for legacy browsers. It is a perfect fit for chat apps. Not sure how far you are into the backend development, but wanted to point out this competitor in case you hadn’t heard of it. .Net is cross platform, has a good ORM, and a ton of industry support as well. Kestrel performance is fantastic.