Code (C++)

bool     Bool_var;
uint8_t  temp = 0x7f;
uint8_t  Key = 0;
uint8_t  OldKey = 0;

void setup() {
	Serial.begin(115200);
	while (Serial) { ; }
   
	*(uint8_t*)&Bool_var = 0xff;	// initially here was restoring a variables from EEPROM, which wasn't initialized!

	pinMode(0, INPUT_PULLUP);	// hardware button connected to pin 0
}

// the loop function runs over and over again until power down or reset
void loop() {

	Key = digitalReadFast(0);				// reading the hardware button and try to invert the bool variable on each pressing
	if ((Key == 0) && (OldKey == 1)) {			//
		//Bool_var = Bool_var ? false : true;		// initially i saw issue in this expression, but during the studying
		                                                // of the problem, I changed the code to one that is not commented out.
		temp = Bool_var ? 0 : 1;			// if I change this expression, to use other values, not just 0 and 1,
                                                                // everything starts to work perfectly.
		//temp = Bool_var ? 0 : 5;                      // For example, this expression works fine.
		Bool_var = (bool)temp;

		Serial.printf("temp=%i; Bool_Var=%i; ", temp, Bool_var);    // output results to terminal
		if (Bool_var)  Serial.printf("Bool_Var=true;\n");
		else           Serial.printf("Bool_Var=false;\n");
	}

	OldKey = Key;
	delay(10);
}