When I got my first M&P 340 (I have a pair), I ran a collection of various .357MAG ammunition through it. My favorite previous duty loads, 125gr SJHP & 145gr STHP, and some odds and ends I'd left over. I also picked some Federal 130gr Low recoil Hydra-Shok to try.
I quickly decided I didn't care to use 158gr loads. The heavier the bullet weight, the more it hammers the palm. Newton's Second Law of Motion comes into play.
The 125gr SJHP and the 145gr STHP were acceptable for wrist torque and controllability ... in my hands.
The Federal Low Recoil 130gr load was the easiest of the ones I tried, but that's within a relative scale. They're
all somewhat punishing. I ran the little pocket mule through a couple of qual courses-of-fire and some drills, and my hand/wrist was done for the day. I couldn't get any of the other instructors to fire more than a single cylinder load of Magnum ammo through it, and a couple of them were ready to stop shooting it before they'd fired that first cylinder load, but I chided them to finish.
Why did I do it? Just because.

To demonstrate to the younger instructors that proper Magnum revolver shooting technique can be used to make the pocket mule tolerable(ish) and controllable. Never said anything about it being fun or enjoyable, though.
I'll say this, I've fired the occasional PD using Magnum loads, and they're worse for felt recoil, being lighter than the M&P's. Relative scale, though. Pain is still pain.
Nowadays I only fire 1-2 cylinder loads of some old recycled Magnum carry loads through either of my M&P 340's, and that's to finish a qual/LEOSA session after running assorted +P and standard pressure loads through it for the course-of-fire. I mostly carry +P, meaning Speer 135gr +P GDHP, Winchester 130gr +P RA38B and what's left of my stash of Remington 125gr GS, and sometimes even some standard pressure 110gr Hornady CD/FTX (which I actually put back to carry in my 37DAO Airweight, since it's built on the old Airweight aluminum frame, but which is a tack-driver and mild-shooting load in all of my J's

).
Sure, using Magnum loads in the sub-2" J-frame barrel
does offer some velocity advantage. Chrono testing continues to show that. Is it worth the hammering against the palm and the wrist snap, as well as the way the distal knuckle of the trigger finger gets hammered by the rising trigger guard? Does it cause significantly slower recovery between shots? That's something each person has to answer for themselves. I can only offer that it's a bit harder on my hand, now that I've hit my 70's, than it was in my 50's, when I bought my first M&P 340 in '05.
You'll have to decide for yourself.
One of my M&P 340's is presently loaded with 135gr +P GDHP, and the other one is loaded with Winchester 145gr STHP Magnum. I carry a speedstrip or speedloader of the same ammo. Suit yourself.