I mean, directly "mounting" the camera to the phone and shooting with the phone.

This is pretty standard on most decent cameras, although it's usually used with the camera and phone separate. Photographers will set up a a camera on a tripod and use a phone or laptop to control it remotely. It can be used to control multiple cameras.

The youtube and tiktok generation will mount the phone to the top of the camera, usually using the flash mount, and face it forwards. This way they can see the screen while they're facing the camera, and be able to see the framing of the shot while they're shooting.

The biggest problem you'll find is that the phone apps are designed for Android and Apple, or maybe Windows Phone. I haven't used a Linux phone, so I don't know if they run their own apps, or if they run Linux programs. If they run Linux programs, then it's just a case of finding one that controls your specific camera, and has the controls that you want.