You and your friends can compile shared playlists in the web version of Yandex.Music. To learn more about working with shared playlists, go to the Shared playlists section in Help for Yandex Music.
You won't be able to share access to a shared playlist via the app, but you can add tracks to it. All changes to shared playlists are synced with the web version.
Shared playlists that you created are shown in the Minegroup, and playlists that you have been invited to are available in the Favorites group.