I had originally intended to add 4 physical buttons but never ended up doing it. Bart sells a module that works in the Jackpot to help with this. Note that there is only one spot for a module so you couldn’t do this and the FluidDial pendant.
4x Input CNC I/O module from Bart Dring on Tindie
I don’t want to have to run a wire from the Jackpot to any device since I would want to mount this on my table. This means I lean towards doing this wirelessly. Plus, I’m concerned I’ll break something wiring directly.
You can connect an ESP32 wirelessly via a WebSocket or telnet. The WebUI also uses a websocket connection and in general, you should only have one. Telnet allows for multiple connections independent of the websocket connection. Either way, the code for the wireless portion is pretty simple.
I share your appreciation of physical buttons but you could do this pretty easily with a touchscreen like the CYD or similar. Or you could pretty easily use physical buttons with a printed label like you mentioned. Either of these wouldn’t be much code.
Adding in buttons with associated displays gets a bit more difficult, but still possible. You could probably use cheap little I2C OLED displays like these for each button.

Or maybe ones like these and use it to handle 2 buttons:
