It is quite unclear (manual) if it is possible to export private and public keys separately and how to do it.
So, the feature request is: add options to separately export public and private key, or both in a unique file (as it seems to be at the moment).
I run the following on the command line to export separately or a unique file. Cannot understand why unique file exportet via command line differs from the one created as a backup via Kleopatra. Probabily I'm just a dumb dummie.
gpg --output public.gpg --armor --export my_e-mail
gpg --output private.gpg --armor --export-secret-key my_e-mail
gpg --output backupkeys.gpg --armor --export-secret-keys --export-options export-backup my_e-mail