Atlassian Access and Atlassian G Suite integration should share domain claims

Currently Atlassian Access and Atlassian G Suite integration fight for domain claims. I.e an administrator can claim example.com in Atlassian Access, configure Atlassian G Suite integration on a site-level for example.com and lose the claim in Atlassian Access.

Whilst this limitation is partially documented on the Atlassian Access documentation:

Your users authenticate with Google. Because you verify your domain as part of your integration with Google, you can't verify your domain from your Atlassian Cloud site. If you want to verify your domain, you'll need to disconnect the G Suite integration.

This is still highly confusing to customers since they can only manage Atlassian Accounts with the Atlassian Access claim, and the distinction between managed users and users on site is not often well understood.

One scenario is that an administrator blocks a user in Atlassian Access, configures the G Suite integration and hence can not unblock the user anymore. The error message indicates that a user should contact their organization administrator who is then left confused because he will assume that this is a site-level restriction. Whilst this can be easily remedied by an administrator by clicking the re-verify button Atlassian Access, he is going to lose this claim again on the next scheduled G Suite run.