Sending E-Mails from Mac app not possible after adding domain to my Icloud account

I want to provide as much detail as possible so the problem is outlined correctly:

The problem: When I try to send an E-Mail everything seems normal at first (sending sound, blue sending bar loading, option to undo send), BUT no E-Mail is actually being sent.

The "sent" folder remains empty.

No email is sent/ received.

This problem occurred first when I added a new domain to my iCloud account.

To check if it was a problem with the domain I tried the web version of Apple Mail as well. In the web version, I can send E-Mails without issues. The domain is correct and works normally. I can also receive messages normally both in the web and desktop versions of Apple Mail. So the setup of the new domain does not seem to be flawed.

I have not found any help for this problem so far, I hope you can help me to fix this issue.

Thanks!