"when I click on the one with the '22' icon and try to restore the file, it automatically tries to open the client in ProSeries 2022 instead of ProSeries Basic where it was copies from."

Open ProSeries Basic and use the Restore option in the program to restore to the Basic program.

When youre clicking on the file, thats not "restoring it" thats opening it and Professional  is set as the default for opening that file type...so I guess you could go in and set Basic to be the default program to open that file type, but I honestly cant walk you through that, sorry.