Yes, it is a lean-to (shed roofed) struture. The roof ridge joins the existing garage and the roof slopes down and away from there.

So, E.H., it sounds like your approach would raise the frame against the garage,
persuade all the posts and beams up snug against the garage wall, then lag in only the ridge beam to existing studs.

The existing garage's outside wall will become the inner wall of my shop. Panelling will be added as in-fill between my timbers (because in the design -whoops - we forgot to allow for 3/4" t&g between garage wall and timbers).