Hi there, provided that the Time Machine backup files were overwritten with a backup file in a clean Mac, it's tough to tell if they were erased totally or just partially, you can give iBoysoft Data Recovery Software a try to scan the Time Machine backup drive thoroughly for lost files.
In addition, re-utilize the old hard drive on your Mac and see if there is a local APFS Snapshot, which captures all files and folders on your Mac at the previous point, helping you perform data recovery.