Christoph, if you want the Photos Library to shrink immediately, you can start over with an empty library. Once your complete library has finished uploading to iCloud Photos, make a backup copy of the Photos Library on an external drive, then quit Photos and delete the Photos Library from your system drive.
- Launch Photos again while holding down the options key ⌥.
- Keep holding down the key, until the Library Chooser dialog appears and select to create a new library.
- Make the new, empty library the system photo library in the Photos > Preferences > General: Use as System photo Library.
- Then make the library your iCloud Photos Library in Photos > Preferences > iCloud. Enable "Optimize Storage".
The library will initially download from iCloud fully optimized, roughly 10% of the original size, but grow again, if space permits, when you download photos for viewing them.
You did not mention your version of MacOS X. When you download the library from iCloud, the named faces will be missing, if you are running macOS 10.12 or older. It is only on High Sierra or newer, that the named faces are syncing with iCloud. The print projects (photo books, calendars, cards) do not sync with iCloud at all, but they are not supported any longer by Apple anyway.