Is there any way to review all file moves done with Finder?
There’s no need to review since Finder cleans up a bulk move almost always and when it doesn’t - you will see the files sitting in the new location.
One way way to know what changes from day to day is Time Machine, so for your peace of mind, set that up and now you’ll have a reliable measure to track files even if they move / delete and even better - you’ll have a backup and not just a record of what was lost or misplaced.