Fix offline recovery after reconnect

[landeqiming666]

Summary

• Restore recovery from offline state when the browser reports it is online again.
• Keep the connection helper from staying stuck in the offline state after a transient network loss.
• Add regression coverage for both the connection helper and background recovery path.

Validation

• PATH=/Users/lijiaxuan/MyInformation/.local-node22/bin:$PATH npm run test:js -- test/connection-test.js test/background-test.js
• PATH=/Users/lijiaxuan/MyInformation/.local-node22/bin:$PATH npm run lint:js
• PATH=/Users/lijiaxuan/MyInformation/.local-node22/bin:$PATH npm run lint:css
• PATH=/Users/lijiaxuan/MyInformation/.local-node22/bin:$PATH npm run build
• PATH=/Users/lijiaxuan/MyInformation/.local-node22/bin:$PATH npm test
• git diff --check

Fixes #132.

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IssueHunt Summary

Referenced issues

This pull request has been submitted to:

• #132: Notifier stays offline despite regaining connection

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[landeqiming666]

Hi, a brief follow-up on this PR. It remains clean and mergeable, and the test check passes. The regression covers recovery after reconnecting from an offline state. Happy to adjust the state transition or coverage.