I just completed a greenhouse and enclosed run addition that connects to my existing coop and garage...so I'm pretty interested in your plans! Last summer I began by building my coop as a lean-to that extends off my garage. I cut a door in the wall of the garage so that we enter the coop through the garage (love this feature in winter!).
Then this summer, on the same wall of the garage but further south, I added a greenhouse a few weeks ago. The greenhouse is about 10 feet away from the coop and inbetween the coop and greenhouse we added a covered, enclosed run. We had several reasons for creating the run, foremost, we wanted to shade the area between the coop and the greenhouse because I was worried about heat build-up from the greenhouse affecting the heat in the coop during the summer when this southwest area gets pretty hot. Then, this enclosed run is my composting spot, my chicken isolation option when broodies hatch chicks, and a way to enclose the flock from predators when we're gone for the weekend (normally they free range during daylight, closed in at night).
I'm not sure but your drawing looks like the greenhouse and coop are both inside the garage? I'm curious how this will work, e.g. sunlight to the greenhouse, heat affecting the chickens? I'd love to hear more about your project and how you're addressing these issues.
Will you be using your chickens, and their manure, to aid in composting? I am amazed at how fast chickens scratching through a pile can speed up the process and am using them to create compost for use in my greenhouse.