I would say in this case, the ATS should probably be sized based on the service rating. Since itís on the load side of the service disconnecting means, IMO, it should only be required to be sized by the actual load supplied, but in your case, with all that excess service capacity, what is to stop someone from adding additional load at a later date.
As far as I know, service rated indicates that the ATS has the AIC rating and is listed as suitable for use as service equipment, not that it is rated at the size of the service.
If itís not likely that the building occupants will need that additional service capacity on the emergency system in the future, one solution might be to install a feeder with OCP sized according to the actual load calculation, or maybe even with some excess capacity, between the existing service and the ATS. Then you could safely size your generator and ATS based on that. You would probably also need to install signage at all panel locations indicating they are also supplied by an emergency standby system.
This arrangement still doesnít prevent someone unqualified from inadvertently adding additional load to the emergency system, but should meet the requirements of the NEC and might save some expense by reducing the size of the ATS, generator, wire size, ground fault indicators, etc. It also leaves the building occupants the option to add additional feeders from the utility supplied side of the service in the future.