The tree is (mostly) off the shed now. Was able to pry the door open and go in for a closer look. The four flourescent light fixtures had fallen on the GT and made a few scratches. The support truss in the middle is partially down, but missed the roof of the GT by a couple inches. Depending on progress made on cleaning up all the branches today, I hope to get the car out and wash it down to see the exact amount of damage. Looks like it fared relatively well.
This building was originally a greenhouse, made of aluminum channel - really lightweight but along with the T-111 siding I put on it, apparently pretty strong. The roof is the original - 30- or 40-year-old translucent fiberglass panels.
Good news is that, of course, we have insurance on the building. Bad news is that the car is not titled yet (still having difficulty clearing that), and thus not insured. Not sure what value the adjuster's going to place on the building, nor the contents, so will have to see what the next move will be. Hopefully the adjuster will be out today.