Sending BTHome sensor data to mqtt

I have several Xiaomi LYWSD03MMC sensors.

I just switched from ZigBee firmware (GitHub - pvvx/ZigbeeTLc: Custom firmware for Zigbee 3.0 IoT devices on the TLSR825x chip) to BLE firmware (GitHub - pvvx/ATC_MiThermometer: Custom firmware for the Xiaomi Thermometers and Telink Flasher) because the battery life is better.

With the zigbee firmware I was able to get the data very easily into mqtt via zigbee2mqtt. However, now the device is seen with BTHome. All the sensor readings come though just fine. Is there a way to expose that information from BTHome to mqtt? (I’m running the mosquito mqtt broker on HAOS.)

BTHome has already broken out the information from the sensors. I just want to be able to access that information via mqtt.

I guess this is supposed to be handled by mqtt discovery as per MQTT - Home Assistant ? But I can’t seem to get mqtt’s discovery to see my BTHome devices. (I don’t see them at all using a tool like MQTT-explorer.)

Looks like this was also asked in Publish json sensor data to MQTT via the mqtt.publish service

Is How send data from home assistant to MQTT? - #6 by claudius and How send data from home assistant to MQTT? - #7 by claudius the way to handle this? Is there no way to populate topics automatically?