By default, the Contacts Sync app syncs your iCloud contacts with Google, even if you have more than just iCloud contacts on your Mac. If you have multiple contact accounts on your Mac, and you want to sync all of them with Google, go to Contacts Sync > Accounts to Sync > Mac, and select "All." Then sync again. If you continue to have trouble, send an email to firstname.lastname@example.org
Due to a macOS bug, sometimes your Google contacts on Mac can fall out of sync with your Google contacts on the web, at https://contacts.google.com/. Thankfully, you can fix that with Contacts Sync. To do so, go to Contacts Sync > Accounts to Sync >Mac, and choose your Google account. Then go to Contacts Sync > Sync > Google (macOS) -> Google (web).