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.
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Co-authored-by: Claude (Opus 4.6) <noreply@anthropic.com>
Co-authored-by: wxiaoguang <wxiaoguang@gmail.com>