But I can’t fix this overlap- If I try to select a uv vertex in order to move it so they are not overlapping, the two vertices get selected at the same time, as if they are one object. This issue is the same when I get rid of the seam. Is this a modelling issue?
The problem is you are creating a flap, so when the mesh is flattened the flap overlaps its neighbor mesh in the UV.
Continue the seam right around the raised area.
Or do the seams on all of the mesh. Something like this…