is it possible to create a smart home with wide functionality, such as controlling lighting, electrical equipment, sensors, etc., using Home assistant and a family of controllers stm32, and use sub gigahertz communication standard?
It would be possible, but HA is not a protocol.
You would need to implement your own protocol for the wireless communication and have some gateway device which connects to HA (for example in the form of a USB stick which plugs into a raspberry pi).
HA will not run on the devices itself, but it can communicate via the gateway, for example via MQTT or the HA API (which also support discovery, which allows for automatic registration of new devices in HA).
However, I would strongly discourage you to do so.
To me this sounds like an awful lot of work and a huge amount of ‘reinventing the wheel’.
The market is saturated with cheap devices and one of the main benefits of HA is that the majority of these are supported ‘out of the box’.
If you have a tight budget I would look into using Shelly (Wifi), Tuya (mostly Wifi) or Zigbee devices, which come around €20 per sensor/light/relay etc.
If you really want to go sub gigaHz, Z-wave might be an option. However the price is considerably higher and there are not so many products for it.
An in-between solution could be to make your own devices while making use of the existing protocols. For Wifi ESPhome is a good option, for Zigbee you could make use of the TI CC2530 and add your own driver to Zigbee2Mqtt.
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thanks for the clarification. I thought about sub-GHz transmitters, as they are energy efficient and wifi in zigbee. And they have better permeability, and potentially smaller sensors. I am considering whether it is possible to create a commercial product on this. Perhaps it is worth “inventing a wheel” for a commercial product. thanks again