This app was mentioned in 19 comments, with an average of 1.37 upvotes
I'm going to suggest giving Mediamonkey a look. It's not the most visually appealing app around, but it seems to check most of the boxes you need.
MediaMonkey downloads and displays lyrics. I think it uses metadata to search. Syncs with MediaMonkey on PC over wifi as well.
https://play.google.com/store/apps/details?id=com.ventismedia.android.mediamonkey
Might need to look I to a media player. Media monkey has a ton of features
https://play.google.com/store/apps/details?id=com.ventismedia.android.mediamonkey
Is there something that works on windows? May be easier to find an app that is comparable to it on Android.
As far as local music files go I've only really put 320 kbps mp3s on my phone for the sake of space, but I've used MediaMonkey and recently the new(ish) foobar2000 Android app.
Both apps come from reliable developers who've been making highly regarded media players for power users since before modern smart phones, both apps are feature/customization oriented, and both support FLAC. MediaMonkey probably has more features likely due to their app being older, but I believe there are some things MediaMonkey requires a Pro upgrade for that foobar2000 (entirely free) will do. foobar2000 has always been freeware in the past (on PC).
What desktop library manager do you use? Is there a companion app?
MediaMonkey can handle 25x that many songs (at least) on the desktop and allow you to easily structure them on Android to play in the MM companion app (or any other player).
Media Monkey for Android has loudness equalization. Play Store Link
I think you have to use the desktop application in order to have loudness equalization, but its worth checking it out.
Edit: The desktop application is not necessary for Replay Gain/Loudness Equalization
I use MediaMonkey, mostly because I can sync my music and playlist from my computer to my phone for free. WiFi sync is available as an IAP. The PC version is also free.
https://play.google.com/store/apps/details?id=com.ventismedia.android.mediamonkey
My favorite is MediaMonkey.
https://play.google.com/store/apps/details?id=com.ventismedia.android.mediamonkey
Media Monkey - not cheap and also has a PC player - not super featured but decent. Store : https://play.google.com/store/apps/details?id=com.ventismedia.android.mediamonkey&hl=en
Unless I am misunderstanding your problem, you want a different android music player than stock - it is up to the music player which tags they sort on (Android itself has no sway over how the players sort), and some are customizable. I would recommend MediaMonkey or Poweramp. Similarly, I would recommend MusicBee or MediaMonkey for PC to syncing your playlists to your phone.
I don't quite understand why you would have/need 300+ playlists - that sounds like a real pain to maintain. I have nearly 200 GB of music and do quite fine with sorting between AlbumArtist, Artist, and Album tags (and the occasional additional tag), although I do agree that iTunes ignoring album artist is terrible.
I've not tried it on Linux, since I'm still managing my music collection on my Windows box...BUT I've been very happy with MediaMonkey for Windows and MediaMonkey for Android.
MM has a mixed rating on Wine, so your mileage may vary.
MediaMonkey for Android is very powerful and user-friendly, IMO.
I am currently using MediaMonkey as I also use the desktop client on PC.
Have you tried MediaMonkey?
https://play.google.com/store/apps/details?id=com.ventismedia.android.mediamonkey
Syncing over Wi-Fi (or USB) works fine for me.