I note my Nest says it's hard wired, so I wonder if the 12 volt from heat link to thermostat also sends data? But not lost connection and the boiler is a level below the thermostat so quite a distance.
When I had a problem and turned the supply off it gave this screen
it is clear enough when something has gone wrong.
However what I found was the schedule that needed activating. I set all the times on the PC, but it seems on the thermostat I need to tell it to use the schedule.
When it is running the colour changes like this
with in this case domestic hot water being on, I note you can use different software, not sure which you are using.
where it says Hallway with circle with 20 in it saying you are home, that's the Nest thermostat, on opening you get
however you can also use Nest's own software, it seems only on the phone does it show TRV head and wall thermostat on the PC they are separate.
As to if heating will auto turn down if I am away and wife home I don't know, as yet not got her phone set up. Could that be your problem, is it picking you your phone is away and turning heating down, I do wish it was a little cooler to be frank, shows between 21°C dinning room and 24°C in living room, think an air con would be better today.