Github Copilot App not shutting down properly

When Github Copilot App starts to fail sessions, one workaround I found is to restart the application. However, this is now failing all the times as the application doesn't come back up when shut down and restarted. I found out that the copilot.exe process remains dangling and prevents the new instance to come up.

Start by reproducing the shutdown and restart flow described in the issue, then inspect the desktop application's process lifecycle around the dangling copilot.exe process. Confirm what prevents the new instance from starting. Done means shutting down leaves no copilot.exe process behind and the application launches successfully again.

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