I think that diagram might have problem.... T and T on a relay usually are 120V/240 high voltage stuff on the other side... and "usually" if you shorted out T and T it turns on the burner/boiler... and does not needed to apply a voltage to it. as oppose to what your diagram suggests. ... not a 24V thing.from my none pro experience... I suspect magic smoke comes out maybe at best case, or kaboom at worse.
C is easy to find... C means common or aka the other leg in the transformer output that is designated as return/negative sort of... ( not earth)... go look at your 24V transformer. trace which one of the wire is the R connected to... The Other wire is C. If you measure the AC voltage between R and C, it should read 24VAC as well...
in general that is how I usually finds them... except in Hydronic valves... its a bit different but almost the same procedure modified to fit.
Problem with "Smart" thermostat is that it draws a lot more current than standard dumb thermostat, some system can't can handle the extra load..especially the one that have a lot of zones... and power hungry valves.. so you might needed a separate transformer and isolation relay....
echobee website have a great support article on isolation relays.. I have used it to add a transformer for my friends 5 zone hydronic heating... YMMV of cause, If it was me, I would figure out what you have first before diving into things... especially what's bought up on post #2, #3..... you mention baseboard, circulating hot water..... older systems uses line voltage. especially things that mention T1 T2 or T T...
*** this is the article .. I got my friend the HVAC duty transformer 40VA and a RIBU1C relay ... in reality you can choose any relay that is 24VAC but I just choose the one made for HVAC stuff so I don't deal with you buy me cheapie component.
https://support.ecobee.com/hc/en-us...ermostat-installation-with-an-isolation-relay