Freeing up space · Temporary files and Storage Studio's own footprint
Why does Storage Studio keep its undo records on my Mac instead of the external drive?
Short answer: So undo keeps working when the fast drive is away. The records are small and never offered for removal; older safety copies of them are moved to your fast drive when it's connected.
So that undoing a move still works when the fast drive isn't there. These are the small records of what was moved and where; without them, Storage Studio couldn't reliably put things back. They're never offered for removal.
They're tiny compared with what they let you recover. What can grow — older safety copies of those records — is relocated to your fast drive when one is available, so it isn't sitting on the drive you're trying to free up. See How much space does Storage Studio use?