First I stumbled across https://www.thingiverse.com/thing:2857697, which offered drawers in a couple of sizes and a few different frame configurations to hold them, all of which are intended to print in vase mode for speed and economy. I then found https://www.thingiverse.com/thing:3046179, which remixed the drawer to include space to include a paper tag.

What if you want larger or smaller drawers, or more than a 4x4 frame? I'm thinking smaller drawers in a frame with more slots would be useful for electronic components on pieces of cut tape, for instance.

A few hours with OpenSCAD later, this is the result. :)

I've pre-rendered drawers and frames in "medium" (40x20x80 drawers, compatible with the things listed above) in a variety of configurations and "small" (18x12x80 drawers) in a 10x10 configuration. Change the parameters near the top of the source code and you can produce whatever size you want. You could probably even make replacement drawers for an off-the-shelf parts cabinet, so long as you feed it the right dimensions.

Notes:

Print with vase mode (or spiral mode) enabled, with 2 bottom layers, no top layer, 0.2 mm layer height, and 0.35 mm first-layer height. With Cura 3.x at least, this should work. If your slicer has trouble, try increasing the gap to 0.1 mm.

For newer versions of PrusaSlicer (and possibly others), if the internal partitions don't show up, set slice gap closing radius (under advanced print settings) to zero.

If your printer doesn't have a 0.4-mm nozzle, you'll probably want to set nozzle_width to whatever you're using.