Currently we enable the persistent terminal/reconnect feature if a terminal is launched by an extension, unlike the env var relaunch where we disable outright because it can cause issues with the extension as it loses access to the terminal upon relaunch.

Relaunching the PowerShell extension right now for example is a bit of a weird experience though because it creates the "PowerShell Integrated Console", and that reconnects upon reload but is no longer managed by the extension.

Before reload:

After reload it is restored, but no longer owned by the extension:

Assigning to March for exploration.

Thoughts @TylerLeonhardt @andschwa?