I can't write/transmit data to blutooth serial with the AT-09 module

Hello,
I bought this extra cheap module from aliexpress, it’s dlaimed as:
“AT-09 !!! ShengYang Android IOS BLE 4.0 Bluetooth module for arduino CC2540 CC2541 Serial Wireless Module compatible HM-10”

This is the link
https://www.aliexpress.com/item/AT-09-Android-IOS-BLE-4-0-Bluetooth-module-for-arduino-CC2540-CC2541-Serial-Wireless-Module/32820135156.html

I’m playing with it and implemented a simple sketch to communicate using the serial monitor, but I’m having some trouble.

I think the wiring is correct because I can connect using the android app “Serial Bluetooth Terminal”, the module responds “Connected”, then I can send text from the app and it’s displayed in the monitor.

The issue is that I if I write any message in the monitor nothing happen, even with AT commands. I’m pretty sure the code is correct, because when disconnected, the module responds “ERROR” to any message.

Another strange behavior is when I try to pair, it ask the code (that should be 123456 from the datasheet), but after enter it it does nothing but stop blinking the let and make it fixed.
With another android device it ask to “check the device app (?!)” and on an iPad it isn’t in the Bluetooth devices list in settings, but on the ios app “BlueCap” it is recognized and it work the same and in android.

here is the code:

#include <SoftwareSerial.h>

int rxPin = 8;
int txPin = 9;
SoftwareSerial bluetooth(rxPin, txPin);

char r;
char w;
bool NL;

void setup()
{
  Serial.begin(9600);
  bluetooth.begin(9600);
}
void loop()
{
  if (bluetooth.available())
  {  
    w = bluetooth.read();
    Serial.write(w);
  }
  if (Serial.available())
  {
    w = Serial.read();
    bluetooth.write(w);
    if(NL){
      Serial.print(">");
      NL = false;
    }
    Serial.write(w);
    if(w == 10){
      NL = true;
    }    
  }
}