When you move your Photos Library to an external drive, the Photos Library will be exactly as before, the albums, folders, metadata, adjustments will remain the same. But you have to use a compatible external drive, as described here: Move your Photos library to save space on your Mac - Apple Support
As your Photos Library is an iCloud Photos Library you will have to make the library your system photos library after you move it. And then enable iCloud Photos again for the moved library.
After you have moved the library and enabled iCloud Photos again for it, Photos will need to sync the library with iCloud and compare the moved library to the photos already in iCloud. This will take a lot of time. Be patient and let the syncing run, even if it takes several days, if your library is large.
If you do not have any projects in your library (slideshows, books) that need saving, it would be much faster, if you did not move your library, but simply create a new, empty library on the external drive and let the empty library sync with iCloud Photos. This will skip the lengthy upload of all photos to iCloud and you will just download the library as it is from iCloud. You will get your library back as it is, only the projects will be missing, but also some named faces might be missing, the faces you added manually, because Photos could not detect the faces.