It was resolved indeed and many thanks to f4Nm1Z9k2P for his friendly assistance
The basic problem was the format of the TXT entry for the mail record in the DNS. It has been mentioned already here in the forum - in the case of some external DNS providers, it is necessary to remove quotation marks and empty spaces of the key for that field.
I had done this, but my Thunderbird Addon DKIM-verifier still indicated a problem (as indicated in the opening post), which made me think that the DKIM settings for my server aren't working.
f4Nm1Z9k2P pointed out to me that the Addon is actually caching old DNS records. After I deleted the file "dkimKey.sqlite" in my Thunderbird profile, the DKIM-verifier shows a positive result.
I am mentioning this here in case another user runs into the same problems. I have written to the developer of the Addon about this problem, and will eventually update this post with additional information.