phigros and cytus II (fans say the sequel is better, but i haven't played it) are high quality. phigros is free (without ads or even DLC, i would highly recommend it); it has a custom charting community, but i haven't tried it out. if you like the game you can buy another one from the same studio called rizline (also high quality). there are a lot of unique games on mobile, so just scrolling through whatever appstore you use could get you results
live-service games like project sekai (colorful stage in the west) could also work, although proseka doesnt have an option to for accuracy scores/rating. i know d4dj does, but it's rhythm game elements arent as high quality (imo, i don't know the popular consensus) and the community is smaller. world dai star is praised for its' gameplay, but i don't know it that well and it doesn't have an english/global server nor translation
if you don't care about fluff and only want the rhythm game part, sonolus is great. it can be hard to set up but it's perfect for people who just like the gameplay and want to get right to it
i would try out a few live-service games to see if one works for you; a lot of them have gacha elements so if you don't like that then sonolus is probably best
let me know if you want more specific recommendations!