Yes, absolutely. You can use a 5V 2A USB power supply like the ones used in phone chargers.
It will “send” whatever it is given on the R terminal as long as it is AC signal.
2 points though I need to mention here:
- The solid state relays used in HestiaPi are electronic relays and not your standard clickey magnetic relay that does not care about the direction of the current.
- The R terminal (along with the C) is actually used to power the HestiaPi unit and also supply the return lines back to the furnace. If you are going to use a phone charger, you will need to make sure the R terminal is not connected any more with the power section on the PCB and it only goes to the relay’s common pin. That means you will have to modify the PCB by cutting 1-2 copper tracks or in other ways. Make sure you know what you are doing otherwise you are risking of frying your Pi or your furnace.
I am not sure the voltage between the 2 wires is actually 0V. 0V in theory means that they are in identical voltage level, so shorting them shouldn’t make any difference.
I believe there are 2 possibilities. A. You have your multimeter in DC mode while the wires have AC voltage difference, or vice versa. B. The voltage difference between the 2 wires is very little and your meter very low tolerance showing it as 0V.
Please come back if you get more info.