HTTP is actually quite malleable, and adding synchronization is easy.

You can add it to your own website with a few simple headers, and a response that stays open (like SSE) to send multiple updates when state changes: https://datatracker.ietf.org/doc/html/draft-toomim-httpbis-b...

...and you can get these features for free using off-the-shelf polyfill libraries. If you're in Javascript, try braidify: https://www.npmjs.com/package/braidify