Quoting https://support.google.com/googleplay/android-developer/answer/10467955?hl=en#zippy=%2Cexceptions
"There is currently no alternative method to provide the core functionality, or the use of privacy-friendly alternatives (for example, MediaStore API or Storage Access Framework) has a substantially detrimental impact on the critical features of the app that are tied to the core functionality."

foobar2000's main functionality is listing and playing music in all audio file formats, not just files that Google recognizes as music.
Because of this, foobar2000 needs MANAGE_EXTERNAL_STORAGE to properly index user's music folder. 
I tried all alternatives to MANAGE_EXTERNAL_STORAGE that Google provided and they were all broken one way or another.

Storage Access Framework:
Usable only with small sets of files, has issues like "listing content of large folder takes 10 seconds to complete".
I used it in past versions of foobar2000 and it was the main source of bug reports (mainly extreme lag doing most simple things). I will not be using it again.
Problems with SAF performance are well known and widely documented on the internet.

READ_MEDIA_AUDIO:
Finds only file types recognized by Google as music, files in less common formats are hidden.
Examples of excluded audio files: Musepack (.mpc), WavPack (.wv), Monkey's Audio (.ape), Tom's Audio Kompressor (.tak), WebM Audio (.weba), cuesheets (.cue), all module formats (.mod .s3m .xm .it and more), all game music formats.
Hides external cover pictures (folder.jpg, folder.webp, folder.png, etc) - to properly index typical music library with external album cover pictures, we'll also need READ_MEDIA_IMAGES.
Prevents reading of archive files, foobar2000 supports direct playback of music from ZIP/RAR/7Z, which is essential for game music and module formats.
Adds annoyance factor of folders with actual files appearing empty, effectively misinforming the user about filesystem contents.
It would be a lot more useful if READ_MEDIA_AUDIO would just give full access to "Music" folder regardless of file types.

MediaStore:
Same issues as READ_MEDIA_AUDIO, hides formats not recognized by Google as music. Didn't investigate further.