MAIL says "this account already exists" and will not connect to it.
There is another, closed, thread 'MAIL says "this account already exists" but it won't connect to it,' which has a good answer, but I didn't really find the answer easy to understand (getting long in the tooth.)
However, I may have accidentally discovered a simpler answer, not sure how to post it.
On my iPad, IOS 15.5, I simply "Shared" a screenshot with another person's email. It asked me for the usual identification for my email address, accepted it, connected it and sent the screenshot and, when I tried my MAIL again, it connected instantly.
Serendipitous.
iPad Pro, 15