Nest thermostat gen 2 won’t turn off furnace
It looks like your nest is wired without the common, so to draw the power it needs, it triggers frequently your heating circuit, doing so, your furnace relay will read a permanent 'call for heat' and won't stop.  So, check if in your wall there is a spare thermostat wire (pick black one if present) and connect it to the 'common' side of feeding transformer, so the nest will be able to get power directly and won't have to trigger frequently the heating circuit just to recharge itself anf finally, your furnace will stay off.

To reduce 'thermostat frying rate' an option (if 24V transformer is bundled with your boiler and you can't replace it easly) is to put a second (external) transformer and connect the stat via relays (you'll need 3 relay for DC with 24V coils) in this case the thermostat will have to operate only on 'auxiliary' relays and worst case is that you'll have to replace often only the inexpensive relays.