Unable to remove an email account from Mail app as listed accounts are all greyed out

I have multiple email accounts attached to the Apple email app. I’m trying to remove one that is no longer in use. The instructions can be followed to a point - I reach the list of accounts to edit but those listed accounts are all greyed out. They can’t be clicked or removed or altered in any way.

[Re-Titled by Moderator]

Original Title: Can’t remove an old email account