Can't add iCloud-Account to mail app

Hello,

I have a MacBook Pro. So far so good.

I'm not able to add my iCloud-account to the mail program. Not talking about Outlook or other programs I mean especially the mail app of OS X.

What I've done:

I went to the system preferences and tried to add my iCloud account there. I have still an @me-address and it's not working. Also with @iCloud.

All fields like Calendars, Reminders, Safari and so on work out but the field for Mail is grayed out (as you can see on the screenshot).

It's also not possible to add the mail account directly in mail. Same result. For other accounts it works!

I'm working with BigSur 11.6.1

Thanks for any help. I appreciate this!

All the best

Peter

[Image Edited by Moderator to Remove Personal Information]