@Angela_Marra
When you migrate your Nest Account to a Google Account (we did so in 2020), you do NOT "add" your doorbell or thermostat to a new Google home. Rather, the cameras, doorbells, and thermostats that were present in your Google Nest "home/structure" in the Google Nest app are still in that same Google Nest "home/structure" in the Google Nest app when you use the "Sign in with Google" option to sign into the Google Nest app using the Google Account to which you just migrated.
In addition, your cameras, doorbells and thermostats that were present in your Google Nest "home/structure" in the Google Nest app should now also be accessible in the same Google Nest "home/structure" in the Google Home app, though not with the same functionality.
Furthermore, if you had a 1st gen Nest Aware subscription prior to migrating, that Nest Aware subscription should NOT have been affected, but--as a 1st gen Nest Aware subscription--it applies only to 1st gen cameras and doorbells. If your new wired doorbell is a 2nd gen Google Nest Doorbell, you would need a 2nd gen Nest Aware or Nest Aware Plus subscription, which cover all 1st and 2nd gen cameras and doorbells in the same Google Nest "home/structure" and have been available since 2019.
Here is a price list of the various subscriptions: https://store.google.com/product/nest_aware?hl=en-US&modal=upgrade-pricing
You should be able to cancel your 1st gen Nest Aware subscription and get a pro-rated refund if you are no longer using your 1st gen Google Nest Hello Doorbell. However, judging from other posts in this forum, doing so might be problematic. You could try going to Settings | Nest Aware in the Google Nest app and see if you are able to do so there. Or you could see if you still have access to https://store.nest.com/account/subscriptions. (After migrating, that 1st gen subscription page automatically forwards us to the 2nd gen subscription page: https://store.google.com/subscriptions.)
If you can't find your 1st gen subscription there, you could try contacting Support:
1. Go to https://support.google.com/googlenest/gethelp.
2. Select a category/product family, and type in a brief description of the issue, then click "Next".
3. Click "Other", then click "Next step".
4. Under "Resources", just click "Next step". (Clicking one of the listed links will bring up a Help page.)
5. Under "Contact options", choose to get a phone call or chat with the team, depending on availability in your country.
