[codex] Fix offline recovery after reconnect

[bpc-oss]

Summary

• restore offline recovery in the Manifest V3 background worker by listening for browser connection changes
• treat API network error failures as offline-state transitions so the badge recovers cleanly after reconnect
• add regression coverage for the reconnect path and harden the reconnect assertions and network-error matching

Root Cause

The current MV3 background worker can render the offline badge, but it does not actively recover when connectivity returns. It also routes fetch-level network failures through a generic error path instead of re-entering offline recovery.

Validation

• npx -y -p node@22 -p npm@10 npm test
• git diff --check

Fixes #132.