That 'stat is seemingly the Sunvic TLX2358.
It now depends on how 'involved' you wish to become with your boiler electrics, but I'll have to take a step back if you decide it's 'deeply'.
What I would suggest to a cyber-fellow is to leave the boiler and its kaput mechanical clock well alone, and to instead focus on the Sunvic. Simply by-pass the clock using 'perm on', and then transfer your interest to the wall 'stat.
First, cut the power. Then either prise off the dial on the 'stat to expose the wiring behind (you can look up the installation instructions for the 2358), or unscrew the whole unit from the wall. That will likely reveal that the unit has a Live, a Neutral, and a Switched Live - and possibly an earth. If so, that will allow you to fit the receiver from a range of Smart Prog Stats in its place, and to have the wireless controller elsewhere - even mounted on the wall beside it.
Since I think you understand what's involved, I'll leave it to you to decide whether this is fine, or to connect directly to the boiler, tapping in to that 'stat cable you have identified.
What Smart Prog Stat were you considering?
Since, according to Evo, that boiler is Opentherm compatible, you may wish to extract the mac efficiency out of it by fitting an OT-compatible Prog Stat instead, like EPH, Salus, and the Drayton Wiser (seemingly recommended), but that's for you to work out