[codex] Add grouped web push badge support

[firewalker06]

Summary

• group agent push notifications under a shared hq:agents notification tag
• mark routine finished-agent notifications silent while keeping input-required events attention-grabbing
• sync unread-agent counts to the installed PWA app badge from both the service worker and foreground Remote UI
• add a standalone web push behavior guide and update Remote Server docs

Verification

• bin/test
• git diff --check
• previous browser smoke check against isolated bin/tycho serve instance