My gun has the interchangeable backstraps, There is a tool that is in the bottom of the grip that holds the backstrap on and is also used to take the gun down. I do not know if that model does as well, but it sure looks like it. What does the owner's manual say?
There is a little sear disconnect lever in the mag well that you can push down with the tool in the grip... you can also dry fire. Both will accomplish the exact same thing. I don't use the tool personally.
None of my M&Ps do what the OP's is doing. Pull back the slide>rotate take down>release slide>fire>slide slides off.
Does it act any different of you push down the sear disconnect as has been suggested?
All that said, I don't know that what yours is doing would bother me too much. How does it function otherwise?
Speed, it works great. I don't actually know what parts must align for that to release so I'm trying to figure out what those are. My other M&P break free instantly as you'd expect so this didn't feel right. I'll replace whatever is the issue if I figure out what it is. I suspect it's one of the springs.
Ok, i have half my answer. Notice the lines that line up when the take down lever is up vs the forward movement when the lever is down. When I pull the slide back to line up where it should be, it releases. That’s the effect causing the issue, now what controls that?
The effect being, the trigger bar is missing the button.
You can try spreading out the trigger bar loop a little. Be conservative as to not break it.
As far as the slide moving forward when the take down lever is down.., I just check 3 of my M&P's and every one of them does that so I'd call it normal.
The only thing i see different in the two M&P I’ve pulled out is how far the trigger pushes back. It’s nearly all the way on the one that works correctly (shield 9mm 2.0). On the 45, which is a 1.0 it only goes about 85% up the trigger bar loop. The problem is the 2.0 trigger and 1.0 trigger differential which may be part of the changes they made. In this case I’d have to move the trigger loop back towards the sear to make it ride higher and that may not be the issue nor how the 1.0 setup works. Idk. It doesn’t seem to be the issue because both level the sear.