P-MOSFET Dropper-Switch - Linear Region
The measured 7V is not incompatible with the observed 5 and 3.3 V outputs in your scheme (see last bullet); it is still working but very inefficient.
The MOS seems to act as a series-connected linear regulator. Maybe it shall protect/regulate when voltage goes up on 24V during charging.
The transistor Q1 may be there just to switch on/off, but I believe it is part of a circuit that regulates and protect from overcurrent (see figure, taken from here).

R2 is evidently a shunt: it is 0.4ohm, that would drop a voltage around VBE values (i.e. 0.5-0.6V) for about 1.4-1.5A; it is consistent with the MOS heating up a lot. However, R2 seems on the "wrong" side, i.e. upstream; but also the MOS is of P polarity (instead of N)...
17V across the MOS is a lot; probably it is designed for minimum VDS. From this the reason for a P MOS; with negative VGS, not subtracting volts from VA (or at least, this is what I guess was in designer's head). Maybe a reference zener you do not see is gone, and the MOS is taking the whole voltage available, going to the minimum VA=7V allowed for the buck-reg to work.


Sorry, no other ideas.