I unwrapped a mesh and the islands cannot be resize, moved, or anything separately. The whole unwrap is treated as a whole as if the whole thing is selected. They're glued. Inseparable. They won't separate. I'm adding keywords here so if this gets solved, anyone else googling for a solution can find it. I've been googling for an hour and can't find anyone else who has encountered this problem.

Edit:

I found a solution. But I don't understand the logic. For this particular project, for unknown reasons, I have to toggle the "Keep UV and Edit Mode Selection in Sync" button and select the islands. Then toggle it again to make the rest disappear and then I can move them independently.

But now I have a new problem. For this particular project, for unknown reasons, it doesn't show the image texture I made. But if I open up my Babochka file and apply the image there, it shows up. I must have skipped a step or pressed a button or something. But comparing the settings between files, I can't figure it out.

Edit 2:

I forgot to put lights in. That's why the texture wasn't showing up. The hat was dark.