Where can I get data for traffic signals, stop signs, and other sign assets/inventory?

Traffic / transportation guy here.

Usually a quick phone call to your state DOT or city planning / transportation planning division will suffice. What you also need are "turning patterns", and lane configurations. Ask for AADT and AADTT counts as well as peak hour counts, and 30 or 15 minute interval counts. in cities where there are weigh in motion classifiers ask for that data as well, as it is important to any transportation data analyst

I've gotten data through Shapefiles, others through excel. and once I collected data tat wasn't digitized. So don't expect jurisdictions to have the same data formats as you.

EDIT

As a heads up, most states would refuse to give you sign diagrams.

Second update, is that they can charge you for the data. They don't charge for the collection, but they do charge for digitizing it. It's weird like that

Try your state department of transportation. Failing that try a FOI request to your city (after all your taxes paid for the data).