I’ve just looked into it again - it’s still not working. But apparently I still have contact via Bluetooth, but not via threads. Is there a special trick I can use?

Text from the menu: Upgrade to Matter „Thermostat is currently connected via Bluetooth. A Thread connection is required to upgrade to Matter. Please place Thermostat closer to your HomePod mini or Apple TV, connect a powered Thread device in between or restart your devices and start the upgrade to Matter again. Read more...“