Mail not delivered to some external email addresses after server-name/domain change

Finally it worked. I resetup the whole DNS-structure defining MX as root @, and updating all DKIM, SPF and _DMARC entries. Now everything works. Thank you very much for your patience but you and Jesse helped me to find out, that, when everything is made correctly from your side, it can be some fault of the hosting provider.

And reorganizing DNS also does really good in such cases.

Best,
Johannes