Amplify Bluetooth Signal for BT BLE Thermostats with Raspberry Pi, openHAB

Hi, I am looking for a device to amplify the signal from BT ble thermostats
https://www.eq-3.com/https://en.homematic-ip....tail/bluetooth-smart-radiator-thermostat.html

For a control panel based on raspberry pi, openHAB. Unfortunately the signal is very weak and does not even reach 6 meters through one wall

It is probably best to put the ESP32 as an amplifier. The ESP32 will pick up the bluetooth signal and push the data through the wifi.

The gateway mentioned is the best solution , especially with two floors.
To start with, however, set your wifi to a fixed channel 1, 6 or 11, both bt and wifi performance should improve.
Scan your network, e.g. download inSIDer, and see the busy channels in your location.

What exact device do you have in mind? Because I'm finding Plates with this chip for self programming and I was thinking of something out of the box.

I don't know if you can find something ready-made.
Here, for example, I found the BLE2MQTT
https://github.com/shmuelzon/esp32-ble2mqtt

that is, so to speak, the ESP32 acts as a device - an intermediary, it transmits data from Bluetooth directly to MQTT. And if you already have MQTT in the server then all home assistant software, openhab can handle it.

The link does not work and the term BT you used has a very broad meaning. It is not clear what kind of communication you mean in this case. In practice, it is not possible to amplify the BT signal in such a general way. You can only use solutions that are good for some specific situations. For example, there are many sensors that send measurements in BLE broadcast packets. These packets can be received and duplicated or forwarded via WiFi or LAN.
Creating an intermediary through which communication is to take place in connection mode is much more difficult. If, in addition, authentication is used, the problem becomes more complicated.