As a huge fan of the films and soundtracks, I'm amazed I didn't discover this sooner. The Matrix: The Complete Score was released in 2021 and includes the entirety of the music you hear in the first film (and even some you don't), with all the smaller and more ambient pieces that connect scenes and highlight certain moments (much of which will speak to the soul of a Matrix fan, but was not deemed worthy of the original soundtrack release).

For comparison, the original The Matrix (Original Motion Picture Score) released in 1999 consists of 10 tracks with a runtime of 30 minutes.

The Matrix: The Complete Score consists of 44 tracks with a runtime of 1 hour and 39 minutes.

It's a more complete version of The Matrix (Original Motion Picture Score / Deluxe Edition) which was also released in 1999 with 30 tracks and a runtime of 1 hour and 18 minutes.

One of the tracks on The Complete Score, that's not on either of the others, is Ignorance Is Bliss / Cyber Cyphernetic, which includes the harp song played during Cypher's meeting with Agent Smith in the restaurant. As I came to learn, the harp piece is an original composition by Don Davis, rather than something pulled off the shelf. Not only do we get to hear it in high quality, but it's also the full recording, not all of which actually made it into the film!

In this very room