how do smartphone keyboard screens function?

Capacitance, in most modern touchscreens.

(There are several different technologies, but that is the commonest in smartphones).

The touchscreen layer has a grid of transparent conductive tracks (like clear "wires"), one set up & down and another side to side (like rows & columns), with an insulating layer between them.

The touchscreen controller scans the grid, sending small pulses through one set of conductors one at a time and measuring how much is picked up by the other set.

If anything conductive touches the screen, it acts like a capacitor plate with the touchscreen conductors at one side of the glass and your finger at the other, changing how much of the signal from the scanning part of the grid is picked up by the other layer.

The screen controller can tell where the touch happens by the coordinates of the row and column it senses it at.

Any program / app can get the present touch data from the touchscreen system, to use with whatever its displaying.

With a keyboard on screen, it matches touch coordinates to the outlines of the key images to decide what you are typing.

See the right hand half of this image for an idea of the sensing grid arrangement:

https://www.eagle-touch.com/wp-content/uploads/201...

From a to z and from 1 to 0