I believe the approach you would use with Home Assistant is to model all of your http-controlled devices using the RESTful integration and then expose the resulting entities to Homekit using Home Assistant’s HomeKit integration (not to be confused with the HomeKit Controller integration).
For example, you would use a RESTful Switch to create a switch.blower and a RESTful Sensor to create sensor.temperature. There is no RESTful Cover so your cover will have to be modeled as a RESTful Switch: switch.cover.
Then you would configure the HomeKit integration as per its documentation. In the config file, you would specify the entities you permit to be discovered by HomeKit.
homekit:
filter:
include_entities:
- switch.blower
- sensor.temperature
- switch.cover
As a point of reference, almost all of my entities are based on the MQTT integration. I have switches, lights, a lock, cover, sensors, climate, etc and use the HomeKit integration to make them all available in HomeKit.