Since you referenced opening and closing ducts.... I will also put in my comments here, I have answered this same way on several other questions and it might also help you here;
The Ecobee in and of itself can help you with what zone you care about for temperature but won’t help you with being able to truly ‘zone’ the house. You can set what sensor(s) you care about in the comfort setting group, from 1 to as many sensors as you have. During the sleep group, I have it only caring about the remote sensor I have in the bedroom.
I actually wanted to zone my house because my bedroom would freeze out during the day while the AC was trying to keep the living room temperature comfortable and then at night, we would overheat because now the living room was fine but the bedroom got hit with the sun during the evening. The Ecobee can with the extra sensors make the furnace care about the other rooms and or average out the house, or at night focus on a smaller number of sensors or even a specific one like I talked about, my bedroom.
I myself wanted more though and have areas that I don’t care about turn off the vents when I don’t care about them or when they reached temperature that would freeze out stop after the room temperature leveled off at the desired point. I went with the Ecobee and Keen Home smart vents https://keenhome.io because they actually tie together and work together to get ‘zone’ effects like I wanted. The smart vents can close off when the room reaches the desired level for that specific room and then open back up when needed. It doesn’t “call for heat” or “call for cool” but if you use an Ecobee sensor in that room, the Ecobee can then call for heat/cold based on average for the house or for that specific room and then the smart vents will use that same sensor to detect and close off the vent when the set level for that room is reached. It is the best way I have found to do this kind of zoning without having my whole system replaced with something more expensive.
I hope that helps.