How do either of these still have any propellent left? If they were originally scheduled to last only four years, how did they manage to get launched with enough propellent to last decades and billions of miles past their original mission?

According to this article from 2003, the probes have enough hydrazine to last until 2034 and 2040:

https://slate.com/news-and-politics/2003/11/what-voyager-1-u...

Edit: this "Voyager Backgrounder" paper from 1980 is terrific:

https://ntrs.nasa.gov/api/citations/19810001583/downloads/19...

The probes were launched with 104 kg (230 lb) of hydrazine. But I'm still not clear why they were so obviously overbuilt for a four year mission.