Wouldn't the heat BTUs and cooling tons be determined by what part of the country this house is in? I would think a 2000 square foot house in Maine would need a whole lot less cooling than one in Florida, but I'm just speculating.
If I was building a new house there is no way I would run my entire electric service through the transfer switch. I would have a small 200 amp disconnect as my service panel, a disconnect that has a 200 amp main, plus 8 to 16 spaces, and feed through lugs at the bottom. Then you feed the transfer switch with the feed through lugs, you can even use a non-service-rated transfer switch.
You would then have the ability to add anything in future which you would NOT want on the generator (such as basement HVAC, pool pump, garage air compressor, electric car charging, pot growing lamps, etc..) without having to use a shed relay or a shedding contactor.
Doing this during new construction will cost only a few hundred bucks, doing it later will be a huge pain and much more expensive.
I don't think that 22kW is overkill at all for the OP's application.
Goofy, There's no way I wouldn't want everything on my system backed up by the genset.
I had a 400a service installed when I built the house. All I had to do was tell the utility what service I wanted, I don't recall any evaluation to determine if I "needed" 400a.
With a 50a branch to the attached garage, 50a to the detached garage, 100a to the shop, 50a to the coach storage building, and 30a to the tractor shed. I also have a 27kw tankless water heater. Along with the heat pump in the house, and furnace/AC on the shop and garage, the load adds up in a hurry.
It's nice that we can still go about life as usual during an extended outage, though I once had to remind my wife, after our 30kW diesel shut down on overload, that she couldn't run EVERYTHING in the house at once. 🙄