Drawer
This is a Fusion 360 design for a lasercut drawer section that fits inside the Billy bookshelf from IKEA, but that should work equally well with any other bookshelf.
Adjust the dimensions
The dimensions have been measured and they're not quite as given in the drawings from IKEA (they tend to be a few millimeters off here and there, so you may have to adjust the dimensions a bit to fit your bookshelf. Note that if you import the F3D (Fusion Archive File) you can adjust the parameters yourself.
Of course, the design is made generic so it should fit any bookshelf as long as you measure the dimensions carefully and type them into the parameter section.
No kerf setting
For now there is no setting to allow for kerf. I'll add that later when I've had some time to test the design.
Disclaimer
Note that the model should be parameter driven, but that I may have made mistakes that will make the model wonky if you alter parameters. If you spot errors I've made feel free to correct them.