The old wiring does not seem right seems as if using 2 - neutral, 1 - line in, and 3 - which the plan shows as N/C but we would normally use the N/O contact, however it also seems as if the plasticiser is leaching out, that green grunge, this can make the insulation very brittle.
I have not seen any domestic boiler using MODBUS, and you will not need the NTC sensor, that is to ensure the floor does not get too hot with underfloor heating, It seems you have the Moes GC version which is a simple on/off contact. It is not what I would call a "Smart" thermostat. The problem with gas boilers is today most have to carefully control the return temperature, and the flame height is altered to ensure the return water is cool enough to gain the latent heat. So every time the boiler turns off, the boiler looses all the heat in boiler through the flue, and when it restarts is does so at flat out setting, so either connection to e-bus or use of some cleaver algorithms is required to reduce how often the boiler switches off, that's the clever bit.
So the smart thermostat works out how much the room temperature normally over shoots, and calculates when to switch off the boiler so it has the largest time possible before turning on again yet keeping the hysteresis to a minimum. Which with a little thought one realises will never really happen. Things like leaving a door open one day and closing the next will upset all these clever algorithms.
So to do a good job one way or another the wall thermostat needs linking to TRV heads, so all the real work is done by the TRV head, there are thermostats which do not link to TRV heads, which are either made for open plan houses i.e. no doors, like Nest, or designed for use with motorised zone valves like EPH, but most link with TRV heads, so at least two zones, my house has 9 programmable TRV heads, unfortunately non link to Nest wall thermostat, and the boiler does not modulate so really not the best control.
The Moes thermostat allows 1°C to 5°C dead zone temperature, this needs matching to the TRV temperature range, but it is rather a trail and error system. The Hive for example links to the TRV and the TRV sends a demand for heat, which keeps the boiler running even if thermostat is warm enough, be it Drayton Wiiser or Honeywell EvoHome these are truly smart thermostats, the Moes may look good and connect to internet, but you will not really gain much compared with old thermostat.
Even the useless Nest has geofencing, the Moes you have to manually alter setting if in the house or not, it does not track your phone and turn on heating when you get near to home, or have a built in PIR to over ride the geofencing if it detects some one is walking around at home.
If your boiler is not modulating then 1°C is rather a lot, most electronic thermostat are set to 0.5°C and for non modulating boilers you can get thermostats which use a mark/space ratio as they approach target to reduce the hysteresis.
I would say not worth replacing the old thermostat if it still works, maybe add some programmable TRV heads, but the Moes is even worse than Nest, and that takes some doing.