Water coming out of shower head without using the diverter
I have seen this many times where a flap of PFTE tape is covering some of the pipe creating the problem even a chunk in the diverter itself , most of the spigot and shower nipples I have installed have only been 1/2” pipe so I doubt it is the size of the pipe but an obstruction causing the issue. I might pull the spigot and slip a pice of 1/2” in and turn on and see if you still have the problem , then make sure nothing got stuck in the diverter and no excess tape is covering the ends of the threaded pieces (it could always be a bad diverter if not plugged) that’s why I would test with a clean pipe.