Thanks for the very detailed and useful reply!
It does look fishy when I'm not allowed access to admin.google.com as you suggested. It says 'admin.google.com is for G Suite accounts only. Regular Gmail accounts cannot be used to sign in to admin.google.com'
In this case I believe they have access to every mail I receive and every photo I store with this account. I decided to never use it because it is too risky.
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