External drives · Checking your drive
What does "Something has changed files we moved to your fast drive that nothing should be writing to" mean?
Short answer: A deeper check found that something Storage Studio moved has changed in size or file count when nothing should be changing it. It may be a manual edit or an app's own update; if not, run First Aid and make sure the drive is backed up.
Storage Studio's occasional deeper check found that the size or number of files in something it moved has changed, even though that item isn't expected to change on its own. It might be harmless — you edited or tidied it by hand, or an app updated its own data — or it could mean a problem with the drive.
Think about whether you or an app changed it recently. If not, run First Aid on the drive in Disk Utility, and make sure you have a backup of the drive. Storage Studio reports this once per item rather than repeating it.