I think it's your usual ripoff BMS, notice there are are extra D2PAK mosfet footprints so those need to be there for over-discharge, over-current protection, as well a control IC. Most of the circuitry is missing to meet all the protection claims. It's just a lowest cost build out of china.
What's there only does some over-charge protection and equalization - nothing else.
The over-discharge protection switch (D2PAK mosfet) is not on the board, so it can do nothing to disconnect the battery to protect it from going flat dead.
LiFePO4 battery min. 2.5V, nominal 3.2V, max. 3.65V
The shunt voltage is well below the zener voltage+the VBE of the transistor, which is not intuitive. The zener rating VZ of 4.7V is at high currents, several mA on the datasheet. This shunt reg runs the zener at low currents, well below the knee on the curve, perhaps at 0.05mA because the PNP transistor amplifies things.
I estimate the shunt at 3.87V at 20mA and 3.93V at 200mA (0.8W each mosfet hot). So it can overcharge the cells- unless the zener is a lower voltage part. You can do a LTSpice simulation, I did not look at how it does when hot or have exact part models.
The SOT-223 mosfet can't get rid of much heat, it's tiny so I said 0.8W or 200mA overcharge at most it can deal with.
The mosfet has a cosmetic defect or blemish but notice the laser etching of the part number was over top. So I would say it's just a lower quality part and did not pop or anything.
I can't see why cell #3 is the one to fail in the two packs. Unless it gets hotter than the rest or they put a weak cell on lucky number 3.