Don't know if I understand what you want to do. IMHO TimerOne is a good library for repetitive tasks, not for one shot events.

You should use Timer1.stop and Timer1.resume() to start the 3 seconds count whenever you press the button. But TimerOne has a known issue: when you use restart or start the ISR is fired immediatly

Here is my version of your code. It waits for button press and then starts timer. After 3 seconds pressed_check is fired and the longPressDetected flas is set. I hope I have correctly interpreted your question

#include <TimerOne.h>
#define pinButton 3
#define POWER_ON_TIME 3UL //Long press in seconds

volatile unsigned long pressed_Time = 0;
volatile unsigned long myTime_button = 0;
volatile unsigned long myTimeOn_button = 0;
volatile unsigned long myTime_pressed = 0;

volatile bool firstISR_Call = true;
volatile bool longPressDetected = false;

unsigned long holdTime = 0;
bool button_state = false;

void setup() {
    // put your setup code here, to run once:
    pinMode(pinButton, INPUT_PULLUP);
    pinMode(LED_BUILTIN, OUTPUT);

    Timer1.initialize();
    // Create an ISR that is called every POWER_ON_TIME seconds
    Timer1.attachInterrupt(pressed_check, POWER_ON_TIME * 1000000UL);
    // Stop Timer1 now
    Timer1.stop();  
    
    //Timer1.attachInterrupt(pressed_check);

    attachInterrupt(digitalPinToInterrupt(pinButton), button_act, CHANGE);
    Serial.begin(9600);
}

void loop() {
    if (longPressDetected) {
        longPressDetected = false;
        Serial.println("Long press detected");
    }
    delay(100);
}

void button_act() {
    if (!digitalRead(pinButton)) {
        myTime_button = micros(); //Flanco de bajada
        firstISR_Call = true;       // Set to true toprevent "phantom" interrupt
        longPressDetected = false;  // Clear long press detection flag
        Timer1.restart();           // Restart timer from 0 - ISSUE: this fires immediatly an interrupt
                                    // causing a so called "phantom" interrupt
    }
    else { 
      myTimeOn_button = micros() - myTime_button; 
      Timer1.stop();
    } //Flanco de subida
}

void pressed_check() {
    // Detect "phantom" interrupt
    if (firstISR_Call) {
        firstISR_Call = false;
        return;
    }
    longPressDetected = true;
    myTime_pressed = micros() - myTime_button;
    Timer1.stop();
}