Were they commissioned to be built by the state or were they private? Who was involved in approving the design? Were the architects paid well? And was there usually one architect, or a team?
Any insight or resources that could help me answer these questions is greatly appreciated.
New Haven's Civil War Hospital is a decent source. The hospital the book focuses on was built by a charitable organization funded by the State of Connecticut in the 1860's. From what I remember there is no reference to how the actual building was designed though.