Does Microsoft Office Home and Student 2016 work on Monterey?

https://office-watch.com/2021/which-office-for-mac-are-ready-for-macos-monterey/

See if this support article can help:

• Upgrade macOS to continue receiving Microsoft 365 and Office for Mac updates - Microsoft Support

I had Office 2016 and it worked fine (no future updates) but I migrated from an older Mac at the time. If you have not purchased Office then get Office 2021 or the 365 subscription to be safe.