If I upgrade to Big Sur on my 2013 MacBook Air, what version of Microsoft Office will run?

Only the 64-bit versions of Office 2016 for Mac (now retired product), current Microsoft 365 applications (subscription), or the single-purchase Office 2019 for Mac. Like Catalina, Big Sur only supports 64-bit applications and that excludes Office 2008/2011 for Mac. The MS Office documents are not affected by the 32/64-bit issue.

There is also the free, 64-bit LibreOffice Suite.

MS Office 2016, 2019 and 365.

Or you can try the free, open-source LibreOffice which can open, edit and save MS Office files to MS Office formats or it's own format. You can try it now before you upgrade the system to see if it would be a viable alternative.