Give Musicolet a try, I recently switched to it after trying a few other players. I think it should be able to do everything that you’re after, you can create, import & export playlists. I also sync my playlists from MusicBee on my desktop to my sd card on my phone & found Musicolet to be one of only a few players that would recognise the playlists properly.
Where did you import your Xperia from? I got myself pretty sold on getting one but totally forgot that Sony don’t sell phones in Aus anymore. Such a shame. I really want an sd card slot & headphone jack.