It depends a lot on how many items are in the list. If there are less than 10000 items in each sorted set you should probably let the client handle the ordering and just do bulk inserts with order index in a denormalised JSON col or something, but after that you probably want something db-native.
What is the use case where your app would need to let the user sort such a large list? I cannot think of any use case. At that point I would let the user set the order field (integer) as it would not be feasible to have a drag and drop UI anymore. That would be cumbersome to use.
It's not 10k but I have Spotify playlists with 4k+ tracks (queue of new albums I listen to as radio at the office) and I always fiddle with the order of the albums at the tail of the playlist.
