customization – Customize the Controls when in Chrome Kiosk Mode

I am using the Google Chrome Kiosk mode to display some internal websites used at our company.
The Android 10 Devices are implemented in Enterprise Mode with Microsoft Intune MDM.

There I can create a Shortcut through the managed Google Play Store – where I can set up the rough appearnce of the kiosk Mode.

So far so good. But I am stuck at customizing it further, which is very crucial in given scenario. – Sometimes its needed to actually close the browser and start with a new session. – But the session should be retained when simply switching to another app for example.

The switching works, but there is no “Exit Browser” button, instead it has “Share” and “open in Google Chrome” features which are not needed and could be also removed.

Any Ideas?