Did it work as an audio CD, the way PS1 games do?

Yes, the game just played it as a regular CD. In fact, if you put a different disc in the drive it would play the tracks from there instead. There were also console commands to change the track, stop the music, loop, or even reload the disc information if you needed to refresh it after swapping CDs.

Yeah, and I remember if you didn't have the audio cable that went from the CDROM into your sound card, you would never hear the tracks. It wasn't your computer decoding the music, the CDROM drive was simply doing the decoding, and passing the audio out into a CDROM input (just a line-level audio signal) on your sound card.

I'd forgotten about those little cables. If I recall correctly, they were small round cables, with maybe four conductors and a little flat connector with a clip?

4-conductor audio, generally.

Later on there was a generation of two-conductor cables that used SPDIF/PCM Audio instead of analog audio for better fidelity.

I vaguely remember CD drives with a headphone jack output!

(E.g. this one: https://pavel.network/using-cd-drive-as-poor-man-audio-playe...)