So I decided to paint it, which is not normally something I do with vintage furniture. This time though, it was necessary! I took my time and very carefully filled in all the damaged areas with wood filler and smoothed the surfaces with extra fine sandpaper. This took a lot longer than you'd think! Some places I just needed to sand carefully.
After repairs were completed, I prepared the cabinet for priming. I took medium- fine sandpaper and roughed the entire surface of both pieces.