What is the thinnest possible floor joist? I have a low ceiling basement. I’d like to replace the current 2×10 wood joists with thinner metal joists to span 12’6″ with a ~L/400 at 40 psi. I’ve found 6″ joists, but is there anything thinner?

Firstly, that L/400 is way too high and should be L/240, and your 40 PSF is only your live load. You need your dead load too or things are going to get difficult.

A 6″ floor in this scenario is using 4×6 beams at 12″ on center or 6×6 beams at 16″ on center.

Yes, there are commercial solutions such as metal decking with a concrete topper. That would get you down to 3″-4″ but is probably outside the realm you want to look at.

If you are willing to rip out your floor to save several inches I suggest looking into going deeper with your basement floor. You’ll probably need an engineer to tell your contractor how to do it, but I think you’ll get a much better result for your money and effort.