ESP32 cannot connect to Arduino Uno via HC-05 Bluetooth module

I'm trying to connect an ESP32 (as Bluetooth master) to an Arduino Uno that has an HC-05 Bluetooth module attached. My goal is to send serial data between the ESP32 and the Uno.

Setup:

• Arduino Uno connected to HC-05 using SoftwareSerial (pins 13 = RX, 12 = TX).
• HC-05 is in slave mode (AT+ROLE=0).
• Baud rate reported by AT+UART? is 9600.
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Arduino Uno code:

#include <SoftwareSerial.h>

SoftwareSerial BTSerial(13, 12); // RX, TX

void setup() {
  Serial.begin(9600);
  BTSerial.begin(9600);
  Serial.println("Arduino ready");
}

void loop() {
  if (BTSerial.available()) {
    char data = BTSerial.read();
    Serial.print("Received from ESP32: ");
    Serial.println(data);
  }

  if (Serial.available()) {
    char data = Serial.read();
    BTSerial.print(data);
  }
}

I used the example sketches from the BluetoothSerial library, "SerialToSerialBTM (ESP32 acting as master)".

I also tried the discover/connect example.

Both examples can see the HC-05 in the scan, but:

When I try to connect, the connection either fails immediately or disconnects after 1–2 seconds.

I never get stable communication, and no data shows up in the Serial Monitor.

What I tried:

• Confirmed HC-05 is in slave mode (AT+ROLE=0).
• Verified baud rate with AT+UART? → 9600 and used this in Uno + ESP32 code.
• Tested multiple baud rates (9600, 38400).
• Used both SerialBT.connect("98:D3:xx:xx:xx:xx") with the HC-05 MAC address and device name.

Sometimes the HC-05 LED shows a brief connection, but it never stays stable.

Question:

Why can't the ESP32 maintain a stable Bluetooth connection with the HC-05?

Do I need to change the HC-05 role or baud rate to make this work?

Is there a recommended example or configuration for reliable serial communication between ESP32 (master) and HC-05 (slave)?