https://livingnewdeal.org/
You can search by state and project time (for example, Roads and Highways). Depending on the project, you may find dates, documents, and so on about when and how it was built. Info is from volunteers on the ground, so it is sometimes pretty cursory.
I think you're right that the coverage is spotty. My father told me that several projects around my hometown of Muncie, IN were WPA or PWA in origin, including several bridges over White River. I hoped to see info on these, but there's nothing listed for Muncie.