If macOS asks for reformatting or automatically changes the drive type for compatibility, it sounds like your external SSD may have been reformatted or had its file system altered when it was connected to the Mac. But don't worry, recovery is still feasible as long as the old files haven't been overwritten by new data.
A trustworthy recovery tool like BLR Data Recovery, Recuva, or Disk Drill is something you could try. It can recover deleted files from a variety of file systems (APFS, HFS+, NTFS, exFAT, etc.) and scan corrupted or formatted SSDs. Just plug in your SSD, perform a thorough scan, and view the data that can be recovered before saving it.