[web] add external 15s heartbeat to socket.io connection (#22853)

* [web] add external 15s heartbeat to socket.io connection

* [web] extend debugging context for client errors

- include performance.now() timestamp for correlating other timings
- include connectionState, especially for new externalHeartbeat detail
- include spellCheckLanguage to check on client-side spelling impact

* [web] remove unnecessary hook dependency

Co-authored-by: Alf Eaton <alf.eaton@overleaf.com>

* Refactor externalHeartbeat

* Add connectionManager to context

* Clear the interval earlier, and on connect

* [web] refactor handling of socket debugging info

* [web] add split-test for external socket heartbeat

* [web] fully remove connectionManager from connection context

---------

Co-authored-by: Alf Eaton <alf.eaton@overleaf.com>
GitOrigin-RevId: fbebe64f8aa207eb4fd4a8f27d522d1cac35f9d4

services/web/app/src/Features/Project/ProjectController.js

@@ -333,6 +333,7 @@ const _ProjectController = {
     const splitTests = [
       !anonymous && 'bib-file-tpr-prompt',
       'compile-log-events',
+      'external-socket-heartbeat',
       'full-project-search',
       'math-preview',
       'null-test-share-modal',