Revert "fix: recover Continue process after unexpected exceptions (#7463)

[exigow]

Summary by cubic

Reverts the previous auto-recovery change and simplifies core process management. Restart now happens in a dedicated manager with clearer telemetry and proper cleanup.

• Refactors
  • Added CoreMessengerManager to restart the core on unexpected exit with exponential backoff.
  • ContinueBinaryProcess accepts an onUnexpectedExit callback and reports exit output to Sentry/PostHog.
  • ContinueProcessHandler now only handles IO and close; removed internal restart/backoff logic.
  • CoreMessenger manages its process instance, adds handleMessage, and supports restart/close.
  • Startup and service wiring updated to use CoreMessengerManager; proxy restart path updated.
  • Removed BackoffCalculator and its unit test.

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[sestinj]

🎉 This PR is included in version 1.13.0 🎉

The release is available on:

• npm package (@latest dist-tag)
• GitHub release

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[sestinj]

🎉 This PR is included in version 1.12.0 🎉

The release is available on:

• npm package (@latest dist-tag)
• GitHub release

Your semantic-release bot 📦🚀