How can I find door hardware to match the fitment of my vintage hardware?
As I mentioned in my comment above it will be very difficult to identify the maker of your old lockset. However. you shouldn't have to if you're simply going to replace it.   It should be relatively easy to find a replacement lockset that will fit this door without too much adjusting of the door. However, you're probably not going to know until you remove the old lockset and search out replacement sets. Take the old lockset with you when looking for a new one. With this type of replacement I think that's a better way to find what will work instead of shopping on-line.
There are always some adjustments that need to be made, particularly to mortise in the lockset stile and the strike plate. The wood looks to be in relatively good shape so you might be able to get away with minor refurbishment such as, if necessary, filling in the old screw holes. I like to use wood splinters or toothpicks and wood glue. That's if you're lucky. You will probably have to relocate the strikeplate which may require some wood repair around the original site of the plate. Good luck.