Q: How to configure Contacts.app with Google Contacts so that labels show up as contact groups?

I'm trying to get the Contacts app on MacOS Big Sur to display my Google contacts correctly. I have the account configured and the contacts themselves show up, but the Google contact tags (what Google calls "labels" and Apple calls "groups") aren't showing up. Further, if I add a new contact group in the Contacts app under "Google" and use it to group several contacts, they seem to be stored locally (they are there after I reboot) but don't get pushed up to Google. Any suggestions how to debug this further?