Looks like I just used the 640x400 canvas size, since that screenshot is the full image. The only 640x400 screen format option in DeluxePaint is "E-VGA - 256 colors" so I guess that's what I used.
I'm trying to remember what I did to get that effect. It looks like I used the "Raster" font. There's a parallax tool, which is what I used to get that "3D" look. Takes some fiddling to figure out how to use it. Requires you to select a "custom brush" out of your canvas, which is the tool that looks like it should be a selection box. Seems like I used the grid tool as well, and actually yeah the grid button is enabled in the screenshot.
It's interesting because the style of this artwork was directly influenced by what seemed like the most natural way to use these tools. So like I said, the super 90s effect was just an accidental product of using 90s software. This is actually a really fun program to play around with. A lot of the tools are mixed together or something so it's kind of tricky to figure out, but it seems like it's actually really powerful.
Also, when I was trying to learn how to use these tools I searched online to see if there were any tutorials, and I found these official guide videos that were ripped straight from a VHS circa 1991.

It's incredible how this is similar to maybe a homemade tutorial on YouTube but it's got a whole different flavor. A whole hour long wow.... It's a literal time machine and it's fascinating to watch just to experience the atmosphere of "back then." Search "deluxepaint tutorial" on YouTube and there's a few of them. Wonder if Adrian Carmack used these tapes to study the tools of the trade....
YouTube link /
Invidious alt
This video is for a different version of the program (DeluxePaint IV for Amiga, and I'm using DeluxePaint II Enhanced for DOS) but a lot of the concepts still apply. The parallax thing is explained a bit after 37 minutes in.