First of all, proceed slowly. Make sure those recovered files are safe. And read my entire post before you start doing things that could complicate your problem.
Second, don’t try to open them directly. *.manager files cannot be opened. If they are your data files, they can only be called by the program.
Third, the way to access the data is to download and install the latest program. Open the program and add the business, importing the old files. They are old enough they will have outdated formats. But the program should convert them automatically to new formats and save them in your application data folder. It will never call the old files, and neither should you. See this Guide for details: https://www.manager.io/guides/8890. You mention multiple files; some of them may be obsolete, some may not be accounting data files but something else. Don’t hesitate to try to restore any file with a .manager extension. Only real businesses will actually import. Depending on what you’ve got, you may end up with multiple versions of the same business. You can remove ones you don’t need per instructions in the foregoing link. Also, see below on cleanup.
Fourth, don’t ever try to open files that have been touched be newer versions of the program with older versions. That can cause loss of data. The program should prevent you from doing bad things, but you never know.
Fifth, after you have successfully recovered your old business(es), read this Guide on how to clean up the application data folder: https://www.manager.io/guides/8394. Or just leave old stuff in the data folder. Manager ignores the obsolete stuff and uses what it needs.
Sixth, let us know how it goes. And ask questions if you have them.