I think the issue is that devices with screens are usually meant to be your window to experience something else. When you get immersed in something, you forget about the device and focus on the experience.
I like playing games, and when I get into a game the focus is on the game itself, not the controller/TV/etc. I’ve had dreams about games, but it’s always me experiencing the game directly and not focused at all on the details of how I’m accessing the game.
I think it’s the same with phone use, but the experiences we get on a phone are harder to imagine as a"direct experience". Things like sending a text message don’t convert well to a fully immersive experience, so I think our brain skips over them.
Every different part of computer setup/OS/resolution/extension/etc is a data point that can be used to uniquely identify you and track your web browsing. Generally any desktop computer will have a unique fingerprint, the only hardware setup I’ve heard of being common enough to avoid fingerprinting is something like using safari on a modern iphone.