How to connect LCD display to a potentiometer

It is not possible to test the module without wiring it to a microcontroller.
When power is applied to the module, the display remains off and uninitialized. In order to turn on the display, you need to initialize the display with certain commands and parameters. After which you can send characters to the display. This requires it to be wired to an intelligent chip like a microcontroller that can carry out the commands to initialize the module.

Edit: There are also other impractical ways to drive these modules as suggested in other posts.

As you suspect, pin 19 must be connected to a potmeter, other side to ground, wiper to pin 4. No value is specified, I always take 10k.

I think page 2 is copied from a display where pin 22 had a function, and the table lateron which lists it as NC is correct. I sell a display that looks a lot like yours, but mine has only 21 connections. You might check the traces to see whether your 22 is connected to something.