There are usually screws for the thermostat cable that comes out of the wall and connects to the thermostat.
This looks like soldered wires inside the thermostat not the terminal screws.
What kind of heating system do you have?
Heat and AC?
Need to see better pics of the wires coming out of the wall.
Those pics look like internal wiring of the thermostat.
Also that Energex thermostat does the same type of functions as a Nest and has app to control it so maybe you should leave it alone.
Their website says they install these in large buildings and hotels.
We appreciate your help here, Houptee.
Poalik, I wanted to follow up and see if you are still in need of any help. Please let me know if you are still having any concerns or questions from here, as I would be happy to take a closer look and assist you further.
We haven’t heard back from you, so I'll be locking this thread in 24 hours. Feel free to create a new one if you have more questions or have other concerns in the future.