How to synchronize a virtual switch state to a device that is triggered by that switch

Check out these links a well. I assume they are still relevant.

Below lists all your automations that are actually local right now. If it isn’t there, it’s because either the device or the smartApp are not part of the “allowed to run local” list.
https://graph.api.smartthings.com/localInstalledSmartApp/list

Below is the list of tested device types that CAN run locally.