I love to do hills, and I've got a very light frame/bike.
2019 Emonda SLR/Sram Red22 eTap, XXX wheels etc.
Under 13.5 lbs with pedals/cages etc.
It definitely makes a difference on hills, but only steep hills & hill climb races (specifically the
Mt. Washington Auto Road Bicycle Hillclimb), for that I get the bike to ~12 lbs.
On rollers & shorter hills with gradients under 5% I can't feel much of a difference from my Domane SLR, which weighs ~18 lbs.
In fact, the Domane feels faster on flatter roads because it's more aero (also has Aeolus 51 wheels vs XXX2's) than the Emonda.
So, just swapping a frame will not likely make much of a difference.
If you really want a good hill-climbing bike, you need everything to be light, and have the bike well under 15 lbs.