What is the extension name for backup files (time machine) ?

ipa are iOS apps.

.abcddb is the Contacts database.

.otf is OpenType Format font.

There isn't a backup file type. The files are backed up as is. They aren't compressed, converted, or any other manipulation.

You didn't mention it, but what I would do before even attempting any so-called recovery software solution is temporarily disable Time Machine backups, and then run Disk Utility First Aid on the Time Machine drive. If it returns a green status, then I would enable Time Machine again, and observe if a subsequent backup finishes correctly.

A Time Machine backup is a mixture of current files, and the consolidations of prior weekly, and monthly backups. How would the data recovery software manage this mixture of different file versions based on different dates? I don't think that it reliably can do so.

Provided the first paragraph, use /Applications/Time Machine and restore the particular file from a current or past backup.