Soundiiz is using the official Apple Music API to retrieve data of your Apple Music account. Unfortunately, the Apple Music API is not returning playlists you could have published under a public profile (curator profile/managed or artist for example). The Apple Music API is also not returning iTunes Smart Playlists.
We are only able to retrieve and display on Soundiiz playlists that are returned by the Apple Music API which is not including these playlists.
This has been already reported by Soundiiz and many other tools to Apple, but not change has been made to the Apple Music API yet...