Is there an electrical component for something between a button and force sensor?
A solution that involves no mechanical travel would be one sided copper sheets or plates that are part of a 'mass' detection setup. An oscillator puts a frequency of 100 KHZ to 1 MHZ on each plate. When stepped on the bodies 'mass' loads down the RF such that the change can be detected.

Even more sensitive is one that picks up on the phase-shift caused by a body on the plate, compared to a second signal that is not phase shifted.

In both cases a LPF and a diode to convert AC to DC would be needed, along with pots to adjust sensitivity. Especially the phase shift type, as it may trigger just by getting close to the plate.

I assume these pads will form a 3 x 3 or 4 x 4 matrix, so you only need row and column drivers and sensors. That makes either 9 or 16 duplicate circuits. You may be able to cheat if you can get a mux like a 74C150 or CD4051 to scan for a changed input, like a keyboard scanner.