After reading the button to delay the execution without stopping action before a

Hello again, Teodor, sorry for delay, I believe (hope) this modification will work the way you want, let me know if not.

#include <Stepper.h>
#include <AccelStepper.h>
#include <MultiStepper.h>

int buttonPullupPin_0 = 11;
int butonPullupPin_1 = 10;
int val_0 = 0;
int val_1 = 0;
unsigned long timeStart;     //NEW
unsigned int timeEnd = 2000; //NEW
bool timing = false, hold = false; //NEW

 AccelStepper stepper(AccelStepper::DRIVER, 4, 3);


 void setup()
{
 pinMode(buttonPullupPin_0, INPUT);
 pinMode(butonPullupPin_1, INPUT);
 stepper.setMaxSpeed(100);
 stepper.setSpeed(90);
 stepper.setEnablePin(9);
 stepper.disableOutputs();
}

    void loop()
{
  val_0 = digitalRead(buttonPullupPin_0);
  val_1 = digitalRead(butonPullupPin_1);
    
  if (val_0 == HIGH)
  {
    stepper.enableOutputs();  
  }
  
  if (val_1 == LOW)
  {
    stepper.runSpeed();   //I want to continue this action until val_1 == hight plus a certain time delay
  }
  if(val_1 == HIGH && timing == false) //NEW
  {
    timeStart = millis();              //NEW
    timing = true;
    hold = true;
  }
  if(millis() - timeStart > timeEnd)   //NEW
    timing = false;                     //NEW
    // NEW___________________________
  if(hold == true && timing == false) // here i want after reading the button to delay the execution without stopping action before a certain time then execute the action that is conditioned by reading this state of butonPullupPin_1
  {
    stepper.disableOutputs();//I want to delay this action against reading (val_1 == HIGH)
    hold = false;  //NEW
  }
}