shelly relays will do exactly what you want. just wire them as disconnected switches. i do this to simulate 3-way switches, but it’ll work just as well to swap circuit behavior.
you can use a homeassistant action if you’re already using HA, or you can have the shellys call each others web api when it senses the switch.
Depends on the specific Zigbee switch, but generally yes.
The magic is in the fact that you can decouple the relay, and use the switch as a sensor that triggers things that may or may not be related to the physical switch position.
The other reason I like it better than a typical “smart switch” is that I can use the shellys with whatever switch I want, so I can have it match my dumb switches and use different colors.