Old iPhoto files won't open

Which version of iPhoto created the iPhoto Libraries?

If the iPhoto Library has the version 7.1.2 or older, it needs to be prepared with the iPhoto Library upgrader tool, before Photos can open it: Using the iPhoto Library Upgrader tool - Apple Support

But this tool cannot be used on a Mac with Catalina. You will need to use a Mac with an older system version.

A 2010 iMac should have come with iPhoto '09, version 8.x.x. or later. Photos should be able to open these libraries.

But you cannot open the library as a part of the backup, if it is a Time machine backup.

Try to restore the library from the backup to your Pictures folder or another volume, see: iPhoto '11: Restoring from Time Machine with iPhoto '11 (9.2 or later) and OS X Lion 10.7.2 (or later) – Apple Support

Do you mean libraries?

How are you trying? What happens when you do?