PCF 8591 switch using transistor
The issue is the voltage drop on R2
I suppose the module schematic is similar to this one:

The current consumption is is the sum of th currents through

LED-s ~4mA if the module is like the one in the picture, 2mA if using 1K resistors, you can see on the back
POT1 ~ 0.33mA , i can see in the picture it is a 10k pot
R3 and R4 ~0.33mA together at most
R7 and R8 ~ 1.4mA

I total will be a maximum of 6mA which will translate in 5mA*330ohm = 1.65V voltage drop on R2 (from your schematic) that would leave only 3.3V - 1.65V = 1.65V  for the board ( the real value is a bit higher since the current will drop when the supply voltage drops.)
You should lower the value of R1 accordingly only to not endanger the transistor with power on surge current
The maximum collector current of 2N2222 is 600mA , the minimum value for R2 will be 3.3V/600mA = 5.5ohm
The maximum value is given by the maximum voltage drop on R2 let's say 300mV to leave 3V for the AD module than Maximum value for R2 will be 300mV/5mA = 60ohm
It's a good practice to keep the same ground and to switch Vcc rather than GND.



simulate this circuit &ndash; Schematic created using CircuitLab
About using the GPIO to supply the module without the transistor there are 99.9% chances that it can work better than with transistor even not needing a current limiting resistor because the GPIO output saturation limits the current at a safe value but since is not clearly documented in the datasheet you do this at your own responsibility.