When I initiate the left button press from Home Assistant (or from Zigbee2mqtt → Devices), both switches turn on. Digging deeper, I see that 4 mqtt messages are sent for some reason:
Nice! This fixed it for me as well. Thanks for the tip!
My zigbee2mqtt sometimes forgets how to update itself, and it was the case this time. I’ve re-added the repository to my addon store, updated it and now all is well. Thanks again!