Reliably detect whether shell integration is working or not when prepending `PATH`

[karrtikr]

Partially adopt the API listed here: #22128 #20950

The idea is to use the API to run a command and see if we receive an event containing the output

[mkoohafkan]

For PowerShell see also microsoft/vscode#174021

[karrtikr]

@mkoohafkan Thanks, although here we're tackling this issue in a more general way. Your issue should be solved in VS Code Insiders once #22440 is merged.

[karrtikr]

@mkoohafkan Can you please verify the #22418 is fixed in pre-release?