Any reason the high side of the shed roof can’t intercept the existing garage roof further up the pitch? Then you could use open web trusses which although deeper are lighter and potentially cheaper than a wide flange. Attaching them higher also gives you more clear height with a longer span.
That was the original plan. I was going to just extend the existing roof outward, but it would shed rain directly where you have to walk to get to the cars. You’d basically have to walk through a waterfall.