Why is my MacBook Air (Early 2015) not compatible with macOS 13?

Apple chose to make Kaby Lake or newer (7th+ gen CPUs) the cutoff for macOS 13 support. Apple has never published an official "Why".

As for what you can do:

• a: Buy a newer Mac that will support macOS 13, or better yet macOS 15+ for future years.
• b: Switch to using an alternative to Microsoft Office. Teams can be hard to replace, but Pages/Numbers/Keynote are pretty good alternatives to Word/Excell/Powerpoint.
• c: Install Windows 10: I'd suggest bootcamp or a virtual machine.

Current versions of Firefox and LibreOffice will run on Catalina and higher.

Be very careful not to delete your existing copies of Pages, Numbers, and Keynote. The versions in the App Store require Sonoma or higher, so if you were to accidentally delete all of your copies of those Apple applications, and any copies on your backups, you might not be able to get them back.