Hello Sashamaye,
Welcome to Apple Support Communities. We understand that your Playlist doesn't show your recent updates after adding songs.
Do the songs not appear on the playlist or is it only the 'updated' date that appears incorrect? Is there another device that you can try making changes to your playlist from? Also, is there another playlist you can test on your iPhone? This can help isolate where the issue occurs. If you don't have another playlist to test, create a sample playlist using the guidance from How to make a playlist in the Apple Music app.
Take care.