Are the changes in pitch alone, or does the amplitude change as well?
What happens if you set the frequency to something extremely low? I know that 50Hz is unusable, it will flicker, but does something still hum at 50Hz? What about if you increase the frequency in steps until you approach 200Hz?
Your multimeter couldn’t measure anything when you went to 25kHz? That may be an issue of the microcontroller not supplying enough current to charge the gate capacitance on the mosfet in time, or not drain it fast enough to turn it off. If you disconnect the esp from the rest of the circuit, can you measure something then?
If yes, then you’ll want to use a push pull pair for driving the mosfet. Or get a mosfet driver, but a bc547/bc549 pair and a bit of passives will be fine, available in through hole, and considerably cheaper.
If no, then either the esp can’t go that fast in this implementation (was it a software PWM?) or your multimeter doesn’t work in that range.