Time Machine backup

Solution 1:

Your last question first! Why no Backups.backupdb?

Until the last 15 months, Time machine formatted the destination drive as HFS+ and placed each backup inside the Backups.backupdb folder. Each backup appears as a folder with all source folders and files inside it. It uses hard links to avoid really duplicating the files in each backup. The hard links (particularly those for folders) are the main cause of backup corruption.

Since Big Sur, new Time Machine backups format the destination as an APFS volume. Each backup appears as an APFS snapshot. Again all snapshots have all source folders and files. The magic of APFS avoids the duplication of files. This is a much more robust storage and in nearly every way is better.

Can you copy files to your NAS?

Yes, but not easily if you want to preserve all the backup history. My advice would be to copy one snapshot to a somewhere on your NAS. This will lose all your history, but will be simple to do. Of course, you don't need to that if you keep the SSD.

Advice

Assuming it does support Time Machine, start a new backup to the NAS.

Keep the SSD as it is until you are confident you will never want its content.