Is there anyone here who could give a brief overview of or recommend some books on the history of botany?
The only thing that springs to my mind before Darwin is a sort of obsession with collecting plants and putting them in botanical gardens.
Was there an actual (proto-) scientific study of them? Or were they largely prestige projects?
Actually, I have a perfect source for you, but it might not be the kind of source that you want! It's a primary source, and one of the most fantastic works we have from Ancient Rome - Pliny the Elder's Natural History, which is one of the major botanical works from the ancient world. If you're interested in their perspective on things (Like his whining about how much money Rome paid to India to import her spices), it's a great read, even if it does get a bit dry at parts :)
Have you looked into Carl Linnaeus? He practically invented the modern field of plant taxonomy in the 18th century. We still use his binomial nomeclature for naming plants.