The software history
The software was made around 1999 to 2001 by Fluid Entertainment (see the back of the cover). The company had the software on their portfolio till around 2013 when the webpage vanished. Around 2003 or such, Wizards brought a different developer in to fix issues and broaden the scope - but those don't seem to be the addition of music. That contract lapsed in 2006.
Fluid Entertainment was founded in 1998, so E-tools was kind of the first steps for them. The company portfolio in 2013 was mostly web-games, and LinkedIn still lists three employees. One of the three employees is described as "recording artist, song writer, classic car builder at fluid entertainment".
With this little information, it appears as if the music was either contracted for or made in-house, but maybe I can take a look at the files itself...
Dissecting the files?
The Fluid-Entertainment Archive
The Webarchive allows downloading the 1.2 files as hosted by Fluid Entertainment. However, this archive doesn't install on a modern machine due to a DirectX error ("The DirectX folder does not exist on your Media"), even trying to emulate an XP machine. The .cab files don't open as cabinet files either. As a result, I can't try to look at the files from data2.cab which seems to be the one that contains the music - if it is there.
The best information we get from this archive without a working installation/installed file is from the Readme.txt:
The computer software, artwork, music, and other components included in
this product (collectively the "Software") are the copyrighted property
of Wizards of the Coast, Inc. ("Wizards").
So, even if Fluid Entertainment was the original source of the music, it was possibly work-for-hire for Wizards of the Coast.
The Archived CDs
However, the 1.2 Demonstration CD also is archived as 1.0 and 1.2 in the Web Archive. These CD images are formated differently and have to be either turned into a physical CD again or mounted in a virtual drive.
The 1.2 Demonstration CD does contain the proper DirectX file, installs and runs on a modern machine! So now the delving in the files can begin:
There is exactly one file in the path
\Wizards of the Coast\D&D Character Generator Demo\Resources\Music: Menu.mp3
However, that file only has very little metadata: a length of 53 seconds, a Bitrate of 128 bit, and created on 28th of April 2000, 08:14. Author or interpreter are missing.
\Wizards of the Coast\D&D Character Generator Demo\Resources\Audio.pak does not compute as a valid archive.
However, there is an answer: The program has a Credits function, and that contains the answer:
Sound Design & Production
Apparently, this is the same Paul Gorman that also made the Forgotten Realms: Baldur's Gate - Dark Alliance soundtrack in 2001, the Neverwinter Nights soundtrack in 2002 and SW:KotOR in 2003. According to LinkedIn, he ran Duff Studios from 1999 to 2003, which would mean he was most likely a contractor for Fluid Entertainment.
In particular, he is credited twice to have made the sounds for the two Pokémon card games made by Fluid Entertainment in 1999 and 2000, establishing that he most likely worked with or for them in the right timeframe. Both these games were also made for Wizards of the Coast as interactive tutorials for these card-IPs.