You should describe in detail for what purpose do you want to have an analog peg-signal?
You are asking for a lot of functionality and you want to have this functionality 2000 times.
This requires some effort. As long as the details are not really clear it is hard to find a good solution.
You have posted a picture of the construction. But this is not all. You want to have certain things as functionality and these details are unclear
You can't expect that the users here will speculate dozens of variants until one variant fits to your imagination.
You have to describe this imagination in detail
you have to describe your budget
you have to describe in detail the interaction between visitors and your device
example-description that shall demonstrate the principle and the grade of details:
I need a 13bit = 8196 steps wide resolution of an analog signal to determine the hight of sound that shall be created if a peg is put into one of the wholes
the frequency shall change with the distance between peg-endposition und peg beeing removed completely
chatGPT shall recitate a poem determined by the position the peg is put into
at the same time the 2000 leds shall show a pxiel version of an iconic pciture with changing colors
best regards Stefan