Not sure if there might not be a legal recourse if they ban access to your email, at least if they don't give you the possibility of downloading an archive of its contents. Because, unless they have deleted it, they have your data in that email.

So, under a GDPR reasoning https://gdpr-info.eu/art-15-gdpr/ do you have a right to a copy of your emails even if they have blocked your account? Unless they have deleted all your data I think it would be a yes.