MBP Mail app never gone online

Hello all, I've got a '23 MBP running Sequoia 5.6.1, but I can't get my iCloud account, or an old college email to get online.

The check mark is enabled, and I can't remove the account because it "is shared by other applications on this Mac." I go to Internet Accounts and turn off iCloud mail, but I still can't delete the account in the mail app.

Thanks for any help!