The thing that surprised me about it is that we let our condo’s construction team use it for some high powered tools a few months ago and it seemed to work fine for them
GFCI outlets can trip for two very different reasons.
Like ordinary breakers, they flip when there's too much current draw = overloaded circuit.
Their special sauce is detecting current "leaking" to earth - a so called
ground fault - the GF in GFCI - that could be your feet on bare earth while you hold some live wires for example
- designed to save your life by turning the circuit off at the switchboard.
Your construction workers probably have regularly inspected gear that doesn't have either leakage or overload so no reason for the GFCI to trip.
OTOH, the PID switches the coil directly in and out of the 110v (or 240v in my case in Australia) circuit. When the resistance coil is hot, it draws a little more current but I'd guess it's probably not
overloading the circuit because they usually only draw a few hundred watts at most.
More likely some
residual current leaking to earth tripping the GFCI - either from the coil itself or the electro-mechanical relays and controllers of the PID. If you can swap a known good coil or PID you may be able to figure out which is leaking.
tl;dr might be a faulty earth leaking coil or controller - whatever it is, best find one that does not leak for your safety.