As
@RandomGrinch says, often the smart thermostat is battery powered, and connects wirelessly to a hub of some sort. Both of my main house thermostats use a hub, often not called a hub, but heat link (Nest) hubR (Wiser) receiver (Hive) but they are mounted near the boiler or motorised valves, not where you want to measure the temperature.
And the device to measure temperature does not always need to be wall mounted, Nest has an option to be USB powered, and Wiser thermostat comes with a stand so it can sit on a table or cupboard, being powered by two AA cells, and in fact don't even need a wall type thermostat, you can use the thermostatic radiator valve direct to the hubR.
As to connecting to phone app, that also varies, both Nest and Wiser have apps that work on the phone, Nest will also work with the PC, but what they can do, and how it does it vary. Nest geofencing only allows you to select Eco and Comfort temperatures, you can't set distance from home, Energenie and Wiser use IFTTT (If this then that) I have not tried to set up Wiser for geofencing.
I don't use geofencing any more, as it takes too long to re-heat my home, recovery time is the new buzz word, how long will it take to reheat your home?
I feel I made a mistake with Nest Gen 3, and now use Drayton Wiser as well, I did not go for the cheaper Hive, as it has a 22ºC limit for the demand for heat from TRV heads (Which is better than Nest which simply does not connect to TRV heads) so paid a little extra for Wiser.
With a modern central heating system, the TRV is king, and each electronic TRV head has its plus and minus features, I have Energenie, eQ-3 and Kasa (TP-link) as yet not got a Wiser TRV head, it is on my to-do list. I made a mistake, I got Energenie TRV heads, thinking I could add Nest, only to find Nest does not, in spite of saying it does, work with Energenie. So I have 9 programmable TRV heads, and non will connect electrically to my boiler, try not to make same mistake as me.
I am not worried about OpenTherm or any other ebus connected system, as my oil boiler can't use them systems.
The problem is you need to balance cost to advantage, the Honeywell EvoHome was one of the first, allowing one to control each room from a central HMI (human machine interface) but to fit all linked TRV heads gets expensive, I got the eQ-3 programmable heads for £15 each in 2019, the Energenie were £80 a pair, Kasa £28, you can have some linked and some not linked, but you need to decide how much is worth spending.