[web] Use Button in join chat button

Summary:
Part of ENG-843
Uses Button in join chat button instead of a plain <button>.

Test Plan: Check if the button looks the same and works correctly.

Reviewers: tomek, atul, abosh, ginsu

Reviewed By: tomek, atul, ginsu

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D5323