Can I wire a 200amp auto transfer switch from one metered service to two 100amp panels?

The answer is yes you can install a 200 amp transfer switch to feed the 2 100 amp panels.

The possible issue becomes code requires the generator to be large enough to handle the load transferred. Your generator being 22kw will probably be fine however the total load transferred may exceed the 91.6 amps of capacity.

An example of this being electric oven drawing 40 amps , electric dryer drawing 20+ amps the water heater drawing 20 amps and now add some lights or a well pump A refrigerator, freezer and the generator could be maxed out.

I usually suggest manual (much cheaper transfer switches) this allows you to turn off the dryer Breaker and something else so the refrigerator/ freezers Can run without over loading the system.

22kw will probably be large enough to run your home and garage but if not large enough some load shedding is required and a mechanical transfer switch would be my recommendation.