I am still running Catalina. May I upgrade straight to Monterey, or should I go to Big Sur first?

I have a MacBook Pro 2019 16" that was on Catalina and I upgraded it to Monterey directly, skipping over Big Sur. There were no issues, I don't expect you will have any either.

Another anecdotal instance: we have a 2016 iMac that was on Sierra. In rapid succession I upgraded it first to High Sierra, then to Mojave, then to Catalina. Then I went from Catalina to Monterey, again no issues were encountered.

I do suggest that you update your existing Catalina MacOS so it is fully up to date before moving to either Big Sur or Catalina.

Also do a complete backup of all your files before any MacOS updates or upgrades.