Nest OAuth consent screen Publishing Status from Testing to Published

Tried to change my app from being in Testing to Published so I do not have to constantly relink it with HA.

Google insist that on the Edit app registration page you have a entry for App domain, Application home page and Application privacy policy link. I placed my nabu.casa addresses here. It i sthe samer as the Authorized domains link.

Then they start the verification process and I get an email that has a banner:

Your Google Cloud Project Nest App (id: nest-app)
    [Action Needed] Verify Domain(s)  

The rest of the message reads:

Hi,
Thanks for your patience while we reviewed your project.

To continue with the verification process, you need to update your project Nest App (id: nest-app) to comply with our requirements.

Domain Verification

Please verify the ownership of the following domain(s):

  • nynabucasaaddresslinkwashere.ui.nabu.casa

Go to the Search Console to complete the domain verification process. The account you use must be either a Project Owner or a Project Editor on Nest App (id: nest-app).

If the listed domain(s) are not required for the project, please remove them from the authorized domains section of your OAuth Consent Screen in Google Cloud Console.

Please note: The project you are seeing is your own.

When you’ve made these updates to your project, please reply to this email to confirm that you’re now in compliance.

If you have any other questions, you can read the OAuth Application Verification FAQ or reply directly to this email.

So… Anything I try seems to be wrong or does not work?

How do I prove ownership of my nabu.casa domain I do not really own?

Were we not supposed to enter our nabu.casa domain in the “Authorized domains” section of the “OAuth consent screen” under edit app registration?

If I try to delete it from the Authorized domains I get:

This domain is used by these client URIs: [ a bunch of stuff here .apps.googleusercontent.com?project=nest-app)]. Client credentials must be updated before deleting.

What do I do next? What did I do wrong? How do I change status from Testing to Published?

Thanks
Rich