Hello Stefan Brieger
HTTP error 400 could be due to incorrect URL syntax, DNS lookup issues, or browser cache problems. Ensure the TXT record is correctly formatted and includes the “MS=” part
https://learn.microsoft.com/en-us/answers/questions/810312/unable-to-verify-custom-domain-in-azure-txt-record
You need to enable Managed Identity on your App Service and assign permissions into the Key Vault to this App Service Manages Identity.
https://stackoverflow.com/questions/68017270/imported-tls-certificate-does-not-show-up-in-app-service
Double-check the correct DNS records and take a look into App Service diagnostics.
https://learn.microsoft.com/en-us/answers/questions/699662/unable-to-verify-domain-name-in-azure-app-services