In the end, the issue on my side was caused by the SFTP server that didn't release the locks that they create. As such, given that Camel tries to delete the files first before uploading them, this deletion fails with "Permission denied". In such a scenario, also downloading of the files fails and only by deleting the locks the situation gets again under control.

Given the above, I was able to reproduce the issue also with WinSCP and the RHEL sftp client.