For years I used a Horstmann DRT2 thermostat, swapping batteries every years it worked great, they would last around two years, so swap every year and fine, if batteries did become discharged it would default off, only problem the depleted battery sign comes on after the point where it stops working, so needed wireless with mothers house so got a Horstmann HRFS1 however this was a problem it would miss the change and both stick on and off, it would not then switch on/off without turning the heat up/down.
The DRT2 was replaced with Flomasta 22199SX which was nearly the same, but extra on/off per day, and can be set default on or default off, the HRFS1 was returned to the Honeywell Y6630D wireless thermostat which default is off, and the batteries lasted around 3 to 4 years, and it always failed off with either flat batteries or anything that messed up RF signal, if no signal every ½ hour it turned off, it also had anti-hysteresis software so as it approached set temperature it started a mark/space ratio so temperature did not over shoot, it had an analogue dial and was not programmable, but was a very good thermostat.
New house using Nest Gen 3 it will work wireless and you can select digital or analogue connection to boiler, I am using analogue as oil fired and also using hard wired connection option, the dial is same idea as computer mouse, so really digital but it looks like analogue, and has a digital display which you can select what it shows, temperature, time, date etc.
As to use with phone, did not set geofencing but found it was auto set, so does auto turn down temperature when I leave the house, however also using Energenie MiHome TRV heads on entrance floor and they also can have geofencing set, but also have anti-hysteresis software which means they take a long time to reach set temperature.
Position matters, 6 am at moment bedroom at 19°C living room 16°C and hall where main thermostat is, 16°C on the TRV but 17°C on wall thermostat, the latter closer to centre of house and higher up. Old house on a sunny morning measured as much as 8°C difference in the same room, depending on if sun hit the area, how close to radiator and if door open or closed TRV would show 20°C but weather station would show 28°C out of direct sun light but near window, in sunlight hitting 32°C. All the instructions show wall thermostat on wall opposite the radiator, if the radiator is on an outside wall this works, but if on inside wall that means thermostat on outside wall so always registered low as wall cools it, with the HRFS1 we could move it, best position was found on a tea trolley 2 foot from radiator, and once we went to electronic TRV heads they were the best control we have every had.
This house the wall thermostat is poorly placed, but since Nest which predicts it still works well.