The easiest thing to do, as others have suggested, is to use iCloud. Set up both computers with iCloud and the same AppleID, and store documents that you want to share on iCloud Drive. (Note that if you share your Photos Libraries using iCloud Photos, you'll get to photos using Photos, rather than using iCloud Drive.)
You can sync other things (like your Calendar, Contacts, and Notes) through iCloud, which is pretty handy when using a Mac and an iPhone.
If you're open to using LibreOffice (a free office suite), I believe the current version of it will run on anything from macOS 10.14 Mojave (what you're using now) on up.
https://www.libreoffice.org/
That's one way to address the "app version" issue that Mr.Johnson pointed out. But I believe that in the case of Microsoft Office (or shall I say, Microsoft 365) current versions of the applications probably let you read & save documents using formats known to older versions of Office.