When it is first plugged into power, Sleep Analyzer will be discoverable via Bluetooth for 30 minutes so that it can be set up. After the setup, data is transmitted via Wi-Fi and the device is no longer discoverable via Bluetooth.
Sleep Analyzer does not maintain a continuous Wi-Fi connection with your router. A Wi-Fi connection is used during the setup, and to transfer data as needed. Sleep Analyzer doesn't emit Wi-Fi signals while you sleep. However, it emits short-burst Wi-Fi signals to trigger IFTTT events when you get in and out of the bed.
https://support.withings.com/hc/en-us/sections/6215955439505-Sleep-Analyzer-EU-ROW
https://support.withings.com/hc/en-us/sections/115004090988-FAQ-EU-ROW