I don't know, but you could use mopidy or mpd to accomplish this.

Does this rely on tagged files? The music I'm interested in using is live shows from The Grateful Dead and Phish, and is all labelled in folders and filename. Last time I tried mpd, everything needed to be tagged.

Most clients I've used allow you to browse the library via the filesystem, even allowing you to use that as the default.

Likely not so simple.

You'd have to run the browser on the pi, which is no problem, but then you need a was to access that browser from the outside.

My goal is to use the pi as a car audio player with a USB SSD. Put the pi's wifi in AP mode. Connect a phone to the pi. Now the phone is the UI, but the audio plays through the pi, into the car's aux input.

Not at all what this was made for, but that could be a fun project and also not especially complicated (spawn mplayer on the pi)

Does this maintain any state? Lets say I start playing an album, then leave the page. Does the music restart from the same track/time, when I return, or do I need to reselect the track and start from the beginning?

Nope, the state is all in the audio player component of the browser, this is really nothing but an interface to tell the browser what file to play