Not working with Bluetooth Proxies (ESP32 based)

[bcutter]

While I was lucky to initialy set up this integration without any issues (https://github.com/GrumpyMeow/sonicare-ble-hacs/issues/2#issuecomment-1715326758), I discovered by manually reloading the integration that:

• it will find the toothbrush just fine if it is pretty close to the Home Assistant server - a Raspberry Pi 4 which uses native Bluetooth
• it will NEVER EVER find the toothbrush if next to a Bluetooth Proxy (ESP powered, https://esphome.github.io/bluetooth-proxies/) - at the same time it can be discovered using the "LightBlue" app on an iPhone also next to the BT Proxy ESP

So where's the issue? Is it the BT proxy or this Sonicare BLE integration?

I bet this is one of the reasons for the most open "Can't connect to XYZ" issues in this integration, so really worth looking into this @GrumpyMeow! We should probably start asking for the specific bluetooth environment people use. I already found few users stating they are also using Bluetooth Proxy (e. g. here: https://github.com/GrumpyMeow/sonicare-ble-hacs/issues/2#issuecomment-1556674265).