We just purchased TurboTax 2023 from Costco, same as the last 10 years. Found out it does not work on 2013 MacBook Air with Big Sur 11.7. What are my options?

Probably .  Online System Requirements
https://ttlc.intuit.com/community/system-requirements/help/turbotax-online-system-requirements/00/25787

Oh  here's some info on switching to the Online version.

If you used the Desktop program last year here’s How to transfer into the Online version, expand the blue link if you used the CD/download last year
https://ttlc.intuit.com/community/entering-importing/help/how-do-i-transfer-last-year-s-return-into-turbotax-online/00/25953

If you used the Desktop program before you may notice several differences and not like the online version. It has less features and no Forms Mode. You can only do 1 return. Your return is only saved online so be sure to save both the .tax2023 data file and the pdf file to your computer when you are done. In case you need to amend in the future or if you need a copy to get a loan or something. You might not be able to access your online return when you need a copy.

option not yet mentioned:

do your taxes at a friend's house who have appropriate windows or Mac version. 

Bring your CD, install and file. 

Order a premium Pizza as a surprise to your friend.

Goodluck