Process.CloseMainWindow() and Process.Close() are ignored for processes running in terminal

@zadjii-msft is already working on this.

Since Jan 6, 2023.

### Windows Terminal version

1.11.2921.0

### Windows build number

10.0.22000.258

### Other Software

.NET Framework 4.7.1

### Steps to reproduce

Configure Terminal as default terminal application.
Write application (in our case .NET framework 4.7.1 WPF application) that starts some other console process:
`var startInfo = new ProcessStartInfo {
UseShellExecute = false
};
var process = new Process {
EnableRaisingEvents = true,
StartInfo = startInfo
};
process.Start();`

then try to stop this process with the following code:
`Process process = Process.GetProcessById(processId);
if (!process.HasExited) {
process.CloseMainWindow();
if (!process.HasExited) {
if (!process.WaitForExit(5000)) {
process.Close();
}
}
}`

### Expected Behavior

Process is stopped and the terminal tab is closed (same as in the case cmd.exe is the default terminal application).

### Actual Behavior

Nothing happens.