If I was going to do that I would use a motorized zone damper that has two modes: open and close.

Since this one takes a separate voltage wire to do each, you could use a regular Zigbee smart plug that has a 120VAC NO/NC relay wired to the smart plug, and then connect two different hot wires going to the damper. Turning on the smart plug would close the damper and turning off the smart plug would open the damper.

You could use two smart plugs without a relay, one to the open wire and one to the closed wire, but you would risk damaging the motor if both were to turn on at the same time.

https://www.amazon.com/Motorized-Actuator-Electric-Register-Diameter/dp/B07PJHB568

https://www.amazon.com/TWTADE-JTX-2C-Terminal-Quality-assurance/dp/B07FCHQBKG

The damper could be installed in the duct work before the vent, or if you didn't care about looks and you wanted an easier way, just fashion a mount to connect it to the outside of the vent.