Migrate extension to Manifest V3

[showchi]

Summary

Migrates the extension background runtime to Manifest V3 and fixes follow-up issues needed for MV3 behavior.

This includes:

• Move extension background execution to an MV3 service worker
• Add offscreen audio playback support
• Stabilize runtime service messaging across extension contexts
• Use stable context menu item IDs required by MV3
• Preserve unrelated extension storage keys during settings upgrades
• Fix timer restore/alarm edge cases introduced by service worker lifecycle changes

Fixes

• Fix paused focus timers reporting the wrong next phase before a long break
• Fix countdown getting stuck at <1min after device sleep/lid close by expiring when the scheduled Chrome alarm fires
• Fix settings upgrade behavior so timer state and other unrelated local storage keys are not cleared
• Fix context menu creation to avoid unstable generated IDs
• Fix runtime messaging errors when no receiver exists
• Fix offscreen audio playback build/runtime separation

Verification

• npm run test:unit
  • 33 passing
• npm run build
  • build completed successfully
  • existing webpack bundle size warnings remain