Solar load sharing for an MCU
with Vgs(th) = -0.2V, that would mean at some point Vbat(3.7V) +
Vin(3.1V) = 6.8V max going to an ESP32 (until Vin turns MOSFET off)

Two things here: -

Parallel voltage sources are not in series hence the net voltage does not add. There is only one winner when diodes are involved...
Each voltage source (battery and Vin) are coupled to the system load via diodes. That's D1 for Vin and the internal MOSFET bulk diode for Vbat hence only one supply serves up current to the load (apart from leakage current and when both voltage sources are close to identical).


Is the PMOS only used for higher power system loads, e.g. above the 6V
output of a solar panel?

No, it will work at lower voltages provided the \$V_{GS(TH)}\$ of the PMOS is low enough to adequately turn it on when Vin drops below Vbat. But I think you kind of knew that from EDIT #2 in your question.

I assume there will be a voltage regulator at the system end to drop
Vbat/Vin to the required MCU voltage.

There needn't be if the MCU can operate over a reasonable range of supply voltages.