Don't be worry, your datas should already be displayed on Apple Music Web interface.
If you are not seeing your playlists or favorites elements once transferred with Soundiiz to Apple Music, you probably forgot to enabled "iCloud Music Library" in your Apple Music app settings.
If Sync Library in your Apple Music settings is already ON, tun it OFF and turn it ON again.
Finally logout and login again from your Apple Music application / login on Apple Music web interface could also solve the issue.
Reload the cache of your Apple Music application:
For that, open Apple Music application in your device, go to your library and try one of this:
- Create a new playlist manually
- Rename a playlist
- Delete a playlist
- Add/Delete favorite elements
After that you should be able to see whole transfer made by Soundiiz.
Also, the synchronization from Apple Music to the Cloud could take up to 24 hours sometime. That means even if you are seeing your playlists and favorites Apple Music on Soundiiz or web version of Apple Music, it could take some hours to then be synced to your other Apple Music apps (desktop, mobile ...).
If you are not seeing your Apple Music playlists listed on Soundiiz, be sure you have enabled iCloud Music Library and be aware that for new created playlists, it could takes some hours (even days) before the Apple Music API is finally returning us the complete list.