How to handle concurrent HTTP request when using interrupt
Simple: don't do HTTP requests in the interrupt.

It's usually bad to do anything heavy like that in an interrupt.  Instead you should just set a flag in the interrupt (volatile bool) and examine that flag in loop().

volatile bool sendNotification = false;
volatile int notifyVal = 0;

void loop() {
    if (sendNotification) {
        notify(notifyVal);
        sendNotification = false;
    }
}

void handleInterrupt() {
    if ((long)(micros() - last_micros) &gt;= debouncing_time * 1000) {
        notifyVal = digitalRead(interruptPin);
        sendNotification = true;
    }
    last_micros = micros();
}