This case fits very well to an iPhone 13 mini. It isn't exactly perfect (I can't quite figure out where the error is occurring in my workflow, everything seems perfectly calibrated), but it is very close and feels very good when the case is printed in TPU.

The main case file will fit on a phone without the plate, but fits better with it. Make sure your printer's XYZ steps are precisely calibrated. I strongly recommend printing the case in TPU, but it should work in PLA as well (it will just be more cumbersome).

The plate should be a more rigid plastic such as PLA, which will make everything feel more solid. You won't need to glue them together; inserting the phone into the case will hold everything together perfectly.

I've included two variations of the back plate, one to be used as a blank plastic plate by itself, the other as a core for a fabric wrapping (which is smaller, to allow for the tolerances of a thinner cotton-like fabric). T-shirt thickness should be fine. I recommend using UHU glue to attach fabric to the plate.

I've included a STEP file for the blank plastic version of the plate, so that you can boolean your own design to the plate in CAD software if you wish to.