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

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Add a delay ??

  if (val_1 == HIGH) // 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
  {
    delay(5000);
    stepper.disableOutputs();//I want to delay this action against reading (val_1 == HIGH)
  }

Is that what you want / need?

Now delay() is probably not the way to go as it blocks and you might want to apply the principles of blink-without-delay (example code comes with the IDE).