I’ve repaired thousands of damned effects pedals, though not the make you mention.
It does appear to work in a very similar way to the digitec pedals.
Most cheap Wah pedals simply send the signal through a variable resistor whose movement is controlled mechanically on a rack and pinion linkage.
This appears to work by using a metal plate which passes over an oscillator circuit, and this movement varies the frequency of said oscillator, that frequency is then proportionally converted to a varying voltage to change circuit conditions.
Th advantage of this is that there is no physical connection between the foot lever and the electronics, making it very much more reliable, and also more versatile.
I would first start out by checking the voltage regulator, which may well look like a small transistor, which will be located somewhere near the power input lead.
There is usually some number and letter code on it, the last two numbers usually indicate the voltage it is supposed to deliver, I’d guess that this would be around 7Volts, so the number will probably be XXXXX07(the X just represents any letter and numbers)
One of the three pins should be at around 9Volts, and another should be at 7Volts, the last will be around 0Volts.
You may not even need to do this, inspect this device very closely, if there is even the tiniest smidgeon of a crack in it, or even the slightest form of any other damage such as from overheating, then the chances are it has died.
Replacing it may cure the problem, but chances are that some other component has died, taking the voltage regulator with it, it’s also possible that you have connected it at some time to a power supply that that is too much for it to handle.
If you replace it and it does something similar, then it is highly likely that one of the op-amp packages has gone down, of perhaps a logic chip.
I’d be inclined first to go to the manufacturer and get a circuit drawing before moving on, and because you can spend ages trying to find the duff part without decent test equipment, it might be worthwhile locating all the semiconductors and replacing them.
More update, I just read your second post and it might be that the reverse polairyt diode has gone short circuit.This is just a plain old diode that is set to be off when the device is connected to the power supply correctly, and acts as a short circuit when the polarity is wrong, known in the electronics game as the “idiot diode”.
If the pedal is connected the wrong polarity of supply for any length of time it will burn the diode out, and stop the pedal working, look closely at the circuit board near to the power jack and you would probably see it, it will be somewhat charred.