Adopt to using VS Code API to access terminal output #22128

Although microsoft/vscode#145234 isn't available yet, creating an issue so we don't miss to adopt it. It's a pretty important feature for us in the following scenarios:

• Stop prepending to PATH which leads to problems such as: Always prepend to PATH instead of replacing it #21906 (comment) and start replacing it instead.
• Remove the deactivate prompt asking users to install workaround in their .bashrc files: Show notification when deactivate command is run in terminal #22121 (comment)
• Improve reliability of when to show indicator prompt now that we have access to PS1 or other vars in shell
• Clean up other code in our terminal activation service to stop prepending env vars and start replacing it instead
• Reliably detect whether shell integration is working or not when prepending PATH #22439

Make sure to:

• use strictEnv and pass process.env when launching the hidden terminal, to avoid using env collection for hidden terminals: Environment collection should not be applied on hidden terminals (non-windows) vscode#197187 (comment)
  • This is currently not being used for "deactivate" command, make sure to do that:

    vscode-python/src/client/terminals/envCollectionActivation/deactivateService.ts

    Lines 50 to 55 in 61fcf3a

    	const terminal = this.terminalManager.createTerminal({
    	name: `Python ${shellType} Deactivate`,
    	shellPath: shell,
    	hideFromUser: true,
    	cwd: location,
    	});

• avoid adding commands in terminal history where possible, when using these.