I stumbled upon this today, am on 6000.0.31f1. my case was a windowed application and if closed with alt+f4 or the close button from titlebar it would stay in the background. using application.quit works as usual and using the old input system also fixes this issue like NIFFLAS mentioned.

Here is an ugly workaround @Nifflas :

private bool _wantsToQuit;

private void Start()
{
Application.wantsToQuit += () =>
{
if (_wantsToQuit) return true;
_wantsToQuit = true;
return false;
};
}

private void Update()
{
// Workaround for Unity 6 bug :
if (_wantsToQuit)
{
Application.Quit();
return;
}
}

The bug only appears to occur when the new input system is in use. If only the Old input system is in the project, it doesn't.

I'd say this most likely has something to do with interrupting application exit via Application.wantsToQuit or Application.quitting

I'm literally going to need to wait with releasing my game, which is just around the corner, unless this is fixed or I can find a workaround. This needs a fix asap.