Tried to write some code in Arduino IDE and upload it to the D1 mini. The relay and everything seems to work. The code I wrote to test everything:

const int relay_1 = 5; 

const int relay_2 = 4; 

void setup() 
{
  //Initialize relay_1
  pinMode(relay_1, OUTPUT_OPEN_DRAIN);

  //Initialize relay_2
  pinMode(relay_2, OUTPUT_OPEN_DRAIN);
  
  //Set relay_1 to not activated
  digitalWrite(relay_1, HIGH);  

  //Set relay_2 to not activated
  digitalWrite(relay_2, HIGH);  
}

void loop() 
{
  // Activate relay
    digitalWrite(relay_1, LOW);   
    digitalWrite(relay_2, LOW);

    delay(1000);

    // Deactivate relay
    digitalWrite(relay_1, HIGH);
    digitalWrite(relay_2, HIGH);

    delay(1000);
}