thanks for your reply. I noticed this behavior with the cloud shell as well. Haven't tried the solution with powershell so far.
But found some workaround for this problem already. Instead of using "access set", "access update-recursive" does work. The disadvantage here is that if you have a specific sub-folder structure, where not every group of a parent folder should get the rights to all sub-folders, you always have to remove the rights for underlying sub-folders with "access remove-recursive".
For the future, an option like "access update-set", which is not available so far, would be great.
Thanks for your support anyway!