Our central heating also has a wireless thermostat
Other than the ability to remotely adjust temperature set point, display local temperature and indicate heat demand, a wireless thermostat will do very little to make central heating systems more efficient unless they are used in conjunction with other control devices such as zone control motorised valves.
Yes, modern stats usually have slightly adjustable differential but at the end of the day are just on/off devices with variable band width.
Most new build CH installations now incorporate multiple zone control MOV's (motorised valves) which makes more efficient temperature control possible.
My 40 year old CH installation did not incorporate any MOV's or any area stat's, radiators went flat out until the boiler stat cut the boiler & circulation pump.
If a basic room stat was added, this usually just controlled the circulation pump which when stopped resulted in the boiler cutting out due to fast temperature rise (lack of water circulation).
When my hot water reservoir tank developed a leak, on replacement, I had the plumber fit two MOV's which basically segregated the HW and CH systems, big improvement to original but still very basic temperature control with HW tank stat closing the HW MOV (stopping pump & boiler if CH was not active) and CH room stat closing the CH mov (stopping pump & boiler if HW heating was not active).
Did fit radiator thermostatic valves (TRV's) but to be honest think they are a waste of time as they just end up chasing their tails by virtue of being too close to the heat source they are trying to control especially as most plumbers seem to fit them upright with the sensing element as close as possible to the radiator!
With the rise of home automation, what really annoys me is I can't interact or log the data from either of these things.
Don't know anything about smart electricity meters so can't comment.
Remote (Wi-Fi) access to a smart CH stat will only enable remote set point adjustment, may be important if mobility is an issue, display the area temperature and advise if the stat is "in demand" (calling for heat) or not.