@KILIAN GOETZ We understand you are having issues with renewing your app service certificate due to not being able to edit your DNS entries.
If you are unable to add the necessary domain DNS entries required for renewal, please look into mail verification. This will send an email to the domain owner's email address with further instructions.
"Confirm the domain by sending an email to the domain administrator. Instructions are provided when you select the option." Source
Please let us know if mail verification does not work.