Just to add a spin there was another variant of the .357 M&P that was strangely model marked as a 19-3 IIRC.
I look at this version as the blued granddaddy to the 65 Lady Smith with shrouded ejector rod.
In reality it doesn't make sense marking it a Model 19 since it had fixed sites but just pointing it out in case anyone encounters one out in the gun world.