Why do I have this plane and why is my cup, in Object Mode (Principled BSDF, Transmiission=1, Roughness=0) have what looks like an HDRI country scene in LookDev mode?
You do have another plane in your scene, it's just not showing in the viewport.
In your outliner check these options and look at all the collections you have, there is a plane there not visible but renderable. You can disable by object or entire collections.
Nice donut btw!
More about it at: Blender Docs
You have 2 planes from what I can see in your outliner. I'd bet that 'plane.001' is the pink one you see in the viewport. The plane that's cutting through the cup (and it looks like the donut is sitting on) may be in the donut collection - it's showing there are 2 items there and it's not expanded.
The reason you can't see it in the main viewport could be that at some point you hid it and forgot about it. See if alt-H brings it back. If not, check out the donut collection and make sure that the outliner shows it as visible.