Moving your install based on that procedure should actually move all of your setup, including playlists and collections.
The only scenario I can imagine where you might have lost them along the way is if you didn’t disable Settings > [Server Name] > Library > Automatically empty trash after scans before fixing the links to your media. In such a case your server will drop the items incl. manual edits like collection/playlist assignments and add them as new items when finally pointing the library to the correct library folder.