Bluetooth proxy only connects to my HA connected device when setting active: trur

Hi all, I have an old Eve room connecting to my HA yellow via Bluetooth onboard of the CM4. The BT connection has become unreliable recently so I decided to use BT proxy for a change. This is my first time using ESPHome and I’ve two big questions:

1/ So I got a new ESP32 board, installed the proxy via the website installer and kept the generic setting. But the active Bluetooth ate up the Eve Room’s battery and after a few hours, the proxy didn’t update the sensor data anymore. I googled and tried to put the proxy to passive mode as follows:

bluetooth_proxy:
  active: false

Seems the proxy is now passive but in turn doesn’t seem to connect to the Eve sensor, rather the Eve device connects back to CM4 Bluetooth. I checks the verbose log and see the proxy still pings the Eve room with good signal.

Here is a screenshot of before proxy, after proxy with active Bluetooth and proxy with passive Bluetooth. At the moment I’m putting back the active Bluetooth setting so the signal went up.

What can I do to fix this situation and improve the connection? I placed the proxy virtually next to the sensor but there’re no improvement.

2/ I checked the validation code of the proxy in ESPhome and saw this following:

bluetooth_proxy:
  active: false
  cache_services: true
  connections:
  - {}
  - {}
  - {}

I didn’t see any mention’s about connections setting on esphome documentation. What is the setting for connections there? Can I fix the Eve room’s MAC address there for constant connection? Something like:

bluetooth_proxy:
  active: true
  cache_services: true
  connections:
  - {11:22:33::55:66}

Thanks heaps!