2 out of 3 buttons on wine fridge display stopped working
One issue to look for might be loose or broken connections along the switch circuit. If this cooler's control/display system is mounted on the door then it gets a lot of vibration each time the door is closed (or slammed). Over time the solder joints and/or mechanical contacts might fatigue or loosen. Contamination could also be a factor, (have you ever spilled wine on the front panel?)
From the picture it looks as though the metal springs are used to bring the capacitive signal from the outer front surface to the inner control circuitry. The larger flat disk likely gives a wide surface area to better detect a finger pressed up against the front surface.
With the power to the unit unplugged, look closely at both ends of the metal springs.  At the PCB side (solder side) verify that each spring has a solid electrical contact. If the contact is only mechanical check if the contacting surfaces have become loose, tarnished, or contaminated. Clean or tighten as needed. If the contact is a solder joint you might look for cracks.  You could even try to resolder the joint just to make sure. On the larger pad side check if there is a weak mechanical connection. Long term thermal cycling or moisture could also degrade the contact. If it has a soldered connection check for a broken solder joint. If the inner surface of the front panel has contacts these might be contaminated, you might clean this with a cotton swab with alcohol. A capacitive switch usually has a high impedance, so just a slight amount of contamination could cause a short and disable the switch.
Also while looking at the PCB look for any contamination of the PCB itself. Just as the switch contacts are high impedance some of the PCB traces going to the controller chip would be susceptible to high impedance shorts. You might clean any possible contamination with a stiff brush and alcohol, or a circuit cleaner spray.