Add e2e tests for the three server push features:
- **Notification count**: verifies badge appears when another user
creates an issue
- **Stopwatch**: verifies stopwatch element is rendered when a stopwatch
is active
- **Logout propagation**: verifies logout in one tab triggers redirect
in another
Tests are transport-agnostic in preparation for a future WebSocket
migration.
---------
Co-authored-by: Claude (Opus 4.6) <noreply@anthropic.com>
Co-authored-by: wxiaoguang <wxiaoguang@gmail.com>
None of the frontend js/ts files was touched besides these two commands
(edit: no longer true, I touched one file in
https://github.com/go-gitea/gitea/pull/31559/commits/61105d0618e285d97e95044bfb64415f364a4526
because of a deprecation that was not showing before the rename).
`tsc` currently reports 778 errors, so I have disabled it in CI as
planned.
Everything appears to work fine.