I wish I had a proper write-up of this project, but I tried to make something like this in college once. I wanted to make a thing where you could type a word and then letters would move to spell that word. I didn't accomplish that fully, but managed to just get the "moving" functionality sort of working. Let's see what I remember about it...
For the board: I just used a large magnetic whiteboard in a classroom.
For the pieces: I made alphabet letters, kinda like scrabble tiles but ~3x3 inches each, with magnets so that they could stick to the whiteboard.
For moving the pieces: I followed various online tutorials (I forgot which) to make an XY plotter, kinda like this:
https://www.instructables.com/XY-Plotter-Drawing-Robot-Ardui...
I used two stepper motors that were somehow attached to the whiteboard using suction cups.
However, instead of moving around a pen that would draw stuff, my XY plotter moved around an electromagnet. This was all controlled by an Arduino and keyboard. So the user could move the electromagnet, turn on the electromagnet to pick up a letter tile, move the letter, and turn off the electromagnet to disengage.
Of course, none of this worked perfectly, but I still learned a ton, and maybe gives you some inspiration!
