With the exception of Tiagra, I don't think there are any modern brifters which work with a triple front mech. I may well be wrong, though (and please correct me if I am). Unfortunately triples have disappeared from modern bikes.
I recently refurbished one of my old bikes for a lockdown project, and ended up putting downtube levers on it for just that reason. My other triple-equipped bike has end shifetrs, so no help there.
However I can tell you from experience that Campag levers work very well with Spyre brakes. I have the Potenza HO levers, which might make a difference (HO = hydraulically optimised, though bizarrely they use cables).