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No one can really answer this question without pictures /maybe layouts.

But as a start, google breezeway.

Had to download the app in order to upload a pic... appreciate your help

You need local design help, and will need measured drawings for bidding and permits anyhow. That said, my first instinct is to extend the house roofline to the garage. The next challenge is to make the two structures appear to be born from the same mother, the house has some contemporary moments while the garage has some Victorian bric a brac.

I agree you need some magic there to make those look like brothers A breezway is by far the easiest way to go If you google breezway between garage and house , you will find tons of ideas and IMO it is the way to go . I can’t see how those 2 roofs could be joinded together in any way that would make sense.I would just use the shed roof to make the join up