Hi @julia1 ,
Welcome to the Auth0 Community!
I understand that you want to migrate users in the google-oauth2 connection to the Username-Password-Authentication connection.
I tried updating the connection type with the PATCH user by id endpoint, but it does not recognize the new connection type. Looks to me this is not feasible.
So I suggest you set up Auth0 Account Linking. With this tool, users can sign up with the Username-Password-Authentication connection and link this account with their Google account.
We have two articles explaining how this works.
https://community.auth0.com/t/how-to-use-the-auth0-account-link-extension-to-link-accounts/81196/2
https://community.auth0.com/t/how-to-implement-client-side-user-initiated-account-linking/81199/2
Meantime, let’s see if anyone else in our community can shed some light on this topic.
Thank you.