I am updating one of my old Android apps where a permission to write system settings is required as:
Intent intent = new Intent(Settings.ACTION_MANAGE_WRITE_SETTINGS);
intent.setData(Uri.parse("package:" + context.getPackageName()));
startActivityForResult(intent, SYSTEM_PERMISSION_REQUEST);
This starts following activity where a user allows modifying system settings:
Things get weird when a device uses gesture navigation in Android 10. Performing a "go back" gesture or tapping the back button (marked on the screenshot) does not return to the application. The settings application is displayed instead.
When using a 3-button navigation or 2-button navigation a "go back" action returns to the application. The only way to get back to the application that seems to work with gestures is performing a gesture that switches between two recent apps.
I've tested this on the device with Android 10 (Android One) and with emulator.