Homekit: multi mode button in home app
Not a complete answer, but here's a list of all accessory service types supported in Apple HomeKit. This defines the entire scope of possibilities in the Home app.

https://developer.apple.com/documentation/homekit/hmservice/accessory_service_types

The accessory categories are:


Light
Power and Switches
Air Quality and Smoke Detection
Temperature and Humidity
Windows
Water
Locks and Openers
Safety and Security
Video and Audio
Information


However, I am not familiar enough with the HomeKit ADK to fully answer your question.