Can a bad USB-C PD charger puff up a battery?
No.
None of the USB specifications involve directly charging the battery, rather they supply power to a battery charge supervising circuit inside the device.
Damaging a battery by overcharging, overdischarging, charging after overdischarging, etc, is the fault of the charge supervisory circuit or a defect in the battery itself, not the external power supply.
That said, it's possible that some faults in an internal battery charger might not reveal themselves if the power supply used were always the limiting factor, but that's far from something you should rely on, especially as overcharging (or otherwise inappropriate charging) could still occur at a low charge rate enabled by a weak supply.
But a &quot;bad&quot; power supply can cause problems - with out-of-spec voltages it could destroy internal circuitry.  Or with a failure of isolation it could kill the user.