A relatively new player app for iOS that seems to be developing well is BTR AMP (by Beyond The Rapids Labs). It is a paid app, with monthly, annual, and infinity options. There is a trial opportunity for the first month, so you have plenty of time to test drive it to see if it suits your player preferences.
The main player window itself has a few options to tailor the colour choices for the accents, as well as background options to work with Dark mode. You can further unclutter this main display window by hiding some of the codec and filetype info. But for the most part it is functional and clean.
The library browser is far more robust than most other iOS players. There are direct access tabs at the bottom for Artists, Albums, Composer, and Genres. Plus a "More" tab to access additional methods to find what you are looking for, and to access to settings. These tabs can easily be rearranged so that the four most common ones can be accessed from the main UI. The list each of these tabs access can be customized in many ways, including a "Favorites" filter that is very handy. Add Artists, albums, or songs to the favorites simply by tapping the heart in any lists, and these are instantly added for quick access. A unique "Featured" tab shows favorite playlists and albums, highlights recently played and added tracks, and even has a most played section.
Adding music for BTR AMP can be done in several ways. It can share your iTunes library of music that may already be onboard your device. Playback of DRM tracks can be enabled (note this will use the iOS Music app for actual playback). One area that may be of interest to those with limited on-board storage is the option to add tracks to your library using the Cloud. Again this will use Apple's Music app for playback. But you can also add audio files directly to the BTR AMP folder and bypass the Music app altogether. This is beneficial to those using FLAC files, since the native Music app still does not support this file type. A recently added "AutoSync" feature expands on ways to transfer music to your device as well, this can be configured to trigger automatically, and access music from a PC or Cloud storage. Google Drive, SMB, and WebDAV (added in v15.2) round out the additional options from within BTR AMP to copy music to your iOS device, without any need for iTunes to be involved.
Overall the UI design of BTR AMP seems to fit well into the iOS world. It is intuitive to navigate and smoothly transitions. There are only a couple of things that stand out that can make it even better. So far the sorting tags are ignored (a key difference from the native Music app), but this looks to be on the radar already as a planned feature in development. Gestures for track next/back or play/pause on the now playing screen would be a welcome addition, hopefully this gets addressed sooner than later for those that are using the player on the road. Since the launch of v1.0 in February 2020, BTR AMP has added many features and is currently at v14.0. I would expect it to continue to evolve, and at this rate it is likely to become one of the best music player options on the iOS platform.
EDIT 1: As of BTR AMP v15 released 2023-02-24
The sort tags are now supported for AlbumArtist, Album, Artist, Composer, and Title. This is a very nice addition and allows the library browser to sort similar to the native Music app.
EDIT 2: BTR AMP v15.1 released 2023-03-20 re:
Gestures for track next/back or play/pause on the now playing screen would be a welcome addition, hopefully this gets addressed sooner than later for those that are using the player on the road
Gestures for track change and play/pause have now been added to the Now Playing screen. This is a nice feature for those using the app on the go. The app can also be set up to automatically switch to the Now Playing screen when selecting any track to play in the browser. Song lyrics can be displayed and edited too. BTR AMP is quickly rounding into a very powerful player for the iOS platform and is highly recommended if you want something far easier to navigate and more robust than the native Apple Music app.