The pedal is connected to Computer's microphone port, which already has 4V supply on the ring. With turning the pot I'm able to put voltage from 0.69 to 3.21 to the jack's tip.
Expression pedal needs to be connected to some device which has connector for such. And this involves more than same kind of plug.
Microphone connector is designed for capturing audio signals. For your expression pedal to deliver such you would need to input it some signal generator, and your expression pedal would adjust volume of signal inputted to microphone jack. Then you would need to somehow convert those signal level changes to midi control messages. Doesn't sound very handy, but might be possible. Most likely you would need to write your own software for it.
To get things working you would need something like this: https://www.audiofront.net/MIDIExpression.php or https://www.kvraudio.com/product/usb-mi ... -tecontrol
See also discussion https://www.kvraudio.com/forum/viewtopic.php?p=6225535