How can I know if my boiler is supported by Nest 3rd Gen thermostat?
Unless you already have a separate electronic controller/programmer for your water heater you can't control it with your Nest thermostat.  Since you haven't mentioned it or provided pictures of a controller or wiring, I assume you don't have one.  Having a controller for your water heater is common in some regions but not in others.  Based on search results from Nest's UK website, I guess it's more common in Europe.  In the southern US, I've never seen a controllable water heater.

A basic water heater is controlled by a knob or adjustment screw and doesn't contain any electronics to interface with.