How does the Bluetooth of arduino uno R4 wifi connect with HC-05?

How does the Bluetooth of arduino uno R4 wifi connect with HC-05?
Can you provide a code case to connect Bluetooth of arduino uno R4 with Bluetooth module HC-05

First of all, the ESP32-S3 does run a special firmware (arduino/uno-r4-wifi-usb-bridge) that exposes WiFi and BLE commands to the Renesas chip on the Uno R4 WiFi board. If your ESP32-S3 firmware is recent enough (otherwise you need to update it), you should use the ArduinoBLE library as instructed in

to program in your needed BLE functionality.

If you need update the ESP32-S3 firmware on the Uno R4 WiFI, see their docs.

However, a HC-05 operates only in Bluetooth Classic mode (source). The Bluetooth-radio of the ESP32-S3 is per https://docs.espressif.com/projects/esp-idf/en/latest/esp32s3/api-guides/bluetooth.html

ESP-Bluedroid for ESP32-S3 supports Bluetooth LE only. Classic Bluetooth is not supported.

So a Bluetooth connection between the ESP32-S3 of the Uno R4 WiFi and a HC-05 module is not possible.

You would need a BLE capable module like a HM-10 for that, see e.g. this video

Of course, if you want to keep the Arduino Uno R4 board but do not want to change out the HC-05 on the other side, you could connect a second HC-05 to the Arduino Uno R4 via UART and pair it to the first HC-05, aka, not using the Uno R4’s native BLE capabilities at all.