Shelly Blu H&T not updating

Hi, I’ve just got a Shelly Blu H&T which I connected with a Shelly Gen3 mini and as soon as I did it popped up in HA as a BTHome entity, which is what I expected. But the values of the entities in HA aren’t changing - just staying at the value they were when the device was added. When I look at the Gen3 mini I can see that they are changing as expected.
It seems like HA isn’t reaching out to update, or the Gen3 mini isn’t pushing the changes to HA. Does anyone know which way around this is supposed to work, and how to get the sensor readings into HA reliably please?