You want to use DS1307 or PCF8563? With DS1307, it has dedicate battery backup pins, so the backup battery voltage doesn’t have to be the same as the supply voltage. In fact, you don’t need to use a supercap, you can use a 3V lithium coin battery, connect the positive to DS1307’s VBat pin, and negative to ground. That way you don’t need the diode and the super capacitor.