I've been trying to find an "offline music player" (that phrase seems to be the best for finding these apps), but the options are dire. There aren't many, not for macOS or iOS. I feel confident in saying that this is because Apple's Music.app is just the best option for music library management for the simple reason that it respects metadata tags - such as something simple like the "sort as" tags! The only other app I have found that does that is Vox.
On macOS, I have resigned myself to using Music.app. Until a library management app comes around that doesn't have weird window constraints and respects the "sort as" tag, I will just keep using Music.app. (Looking at you, Petrichor!) Luckily, you can turn off Apple Music the streaming service and Music.app functions largely as iTunes. On iOS, it's a different story.
I'm looking for an iOS app that includes an equalizer. There are a handful, but they are either expensive, ugly, or both! Here is what I have found and tried:
Cosmos: It's library management is awful. You can sort by artist, but only by track artist, so if you have the album artist and the featured artists in the "artist" tag, you have a complete mess in the artist view. You can view by album, but it sorts by album title alphabetically. There is no option to sort by album artist (and obviously no secondary sort by release year). The music player is fine, though it strangely resists iOS design metaphors (Liquid Glass included, though that's not what makes it standout). I continue to use it because it is not ugly, there is a good equalizer, and I mostly listen to individual albums start to finish anyway, so the sorting is tolerable with the competent search function.
Doppler: This is ideal, the library management is not quite as robust as Music.app, but it's far better than most. However, the app does not have an equalizer.
Jewelcase: Really nice look, only local files, good organization...but only a 10-band equalizer that you have to set with sliders (nightmarish on a touch screen when you're trying to set something to -8.3!), which is better than nothing, but not as good as a parametric equalizer.
Music.app: iTunes, lauded for its library management. As per Apple's design, they are equally as good on macOS and iOS. The macOS app has a simple equalizer, but that's not necessary with SoundSource. The iOS app has no equalizer. The biggest complaint is that, for some reason, the app is doubling all of the lengths of the tracks, but just in the library, not in actual playback. I'm not sure what's causing it.
Pentaton: I'm currently using this. Very simple library, really no management at all, easily navigable. Great, great parametric equalizer, for which you can import settings from a TXT file. Costs 50 USD after trial period.
Vox: This is actually the ideal app: Detailed library management that surpasses Music.app, good equalizer. Costs 5 USD/month or 50 USD/lifetime to be able to access the equalizer.
I'm not subscribing to an app and 50 USD is just...not doable, not right now and not for, frankly, ugly apps.
Music.app is fine on my MacBook; I have an old iPod Touch that I can only sync through Music.app anyway and I'm using a system wide equalizer. But please let me know if you have any leads on iOS apps with good library management and more than a basic equalizer!