@KevinP
There have been several posts in this forum recently regarding the "Caller does not have permission" error message.
In some cases, it was due to the customer trying to use a G-Suite or Google Workspace account instead of a Google (gmail) Account.
In other cases, it seems to be due to the fact that the customer was signed onto more than one Google Account at the same time on their phone or mobile device.
I notice you indicated "Nest app (iOS)" in your post, but the 2nd gen battery doorbell can only be installed in the Google Home app.
If none of this helps, you could try contacting Support; if you get a different solution, it might be helpful to post it, for the benefit of other customers encountering this error:
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.
