refactor(server): Remove unused delay-shutdown REST endpoint

[azmkercso]

Issue

P398067552

Description of Changes

Remove the unused /delay-shutdown REST endpoint and its backing _delayShutdown() method from remoteExtensionHostAgentServer.ts.

This endpoint allowed callers to reset the auto-shutdown timer, indefinitely extending the lifetime of the Code Editor process even when there are no active connections. The feature is not
used by the service — the shutdown lifecycle is fully managed by extension host connection events (_onDidCloseExtHostConnection).

The change is implemented as a quilt patch (patches/sagemaker/remove-delay-shutdown-endpoint.diff) appended to the end of sagemaker.series.

Testing

• Verified all existing patches apply cleanly with the new patch appended (prepare-src.sh code-editor-sagemaker-server succeeds)
• Confirmed no references to delay-shutdown or _delayShutdown remain in the patched source
• Confirmed _cancelShutdown() and _waitThenShutdown() are preserved (still used by _onDidCloseExtHostConnection)
• Expected behavior after the change:
  • GET /delay-shutdown without connection token → 403 Forbidden (previously 200 OK)
  • GET /delay-shutdown with valid connection token → 404 Not Found

Screenshots/Videos

N/A

Additional Notes

• The /delay-shutdown handler was positioned before the connection token validation check, meaning it required no authentication
• The auto-shutdown mechanism continues to work as before — it is triggered when the last extension host connection closes and runs on the SHUTDOWN_TIMEOUT timer

Backporting

This change is submitted as separate PRs against all active release streams:

• main
• 1.1
• 1.0

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