For this, you need to have them as subscribed. If you deleted playlists from your Spotify, now you cam't add them back to your account. I'm sorry! These playlists are not deleted, but them you do not have as "subscribed".
Many years ago you could go to playlist you made, and click a button to add list back to your account. Now it's not possible. I don't know why.
You can't edit the open.spotify.com pages, they are just designed to share a link to your profile (or a single playlist) rather than represent your entire profile. If someone lands on an open.spotify.com profile page it should auto load the full profile in that persons Spotify client.
Just having a look in the client, your public playlists and other details show up perfectly on your profile pages. 🙂