I have a standard (non-combi) boiler with a separate hot water cylinder.
In which case the thermostat likely powers a motorised valve which in turn powers the boiler. As said the two wires go to A and B as shown
with a little luck there is a blue in the cable so link and blue in neutral.
Most instructions say "provide one common electrical supply to the boiler and for the cosponsoring controller."
I have not worked out why with a volt free thermostat this should be required, it seems OK to mix low voltage and extra low voltage in the same thermostat, so see no electrical reason why two independent electrical circuits should not be used, that is clearly what happens with battery powered, and thermostats like Nest have a power supply to give 5 volt to the USB which invariably is not plugged into the same supply as the boiler.
But clearly if independent circuit is used the link should not be fitted.
My central heating now has 10 supplies, one 230 volt and nine 3 volt. When I moved in it had at least three 230 volt supplies two being from different distribution units, with a large sticker saying who installed it, seems even proud of their work.
I would say if possible all central heating should be supplied from one BS 1362 fuse as to if 3 amp or 5 amp depends on how much is supplied. And there should be a means to isolate the low voltage (230 volt) supply. However I can see nothing in BS 7671 which says it must be wired this way, only that manufacturers instructions should be taken into consideration.
The Nest e is about the only thermostat where the base is battery powered. And the Nest e does not connect to TRV heads.
Your the one who should fill in the minor works certificate to say what you have done, and sign it, so your the one to decide how to do it.
I fitted a Nest Gen 3 to my central heating to replace the programmer and re-arranged the wiring so all supplied from one RCBO and FCU. Main reason was so the existing wires only carried low current and extra low voltage (12 volt) from flat under main house to the main house, wires changed colours and no idea where, so don't want low voltage on them.
However the geofencing was switched off earlier this year when the EE mast was damaged in high winds so the system did not detect my phone as being at home. And most the other special features for one reason or another have also been switched off. Non of the so called Smart features are still in use. The linking the TRV heads was first to be switched off. It should have worked, but didn't.
So why bother fitting a Smart thermostat?