The answer
Website and email use different DNS records. A working website does not confirm that mail is configured correctly. MX or authentication records can be missing after a nameserver change.
Mailbox access, storage limits and sending permissions are managed by your email service. atdomain.at can help check your domain and DNS settings.
What to do
Check that the mailbox exists and is accessible at your email service.
Compare MX, SPF, DKIM and DMARC in the active zone with the supplied instructions.
Test sending and receiving with another mailbox and note any bounce messages.
Send support the domain, time and a redacted error message; do not include private message contents or passwords.