I think Star Dates contain meta-information about the actual episode or season number, IIRC. But I doubt they were ever used consistently. In reality, an actual inter-stellar calendar system would have to somehow compensate for the bizarre, counter-intuitive fact about our Universe that “now” is a subjective concept entirely dependent on the location and speed of an observer.
Anyway, yeah the Battle of Endor makes more sense logically as a starting point for the new calendar. From an in-Universe perspective, I don’t know when the new dating system officially began. Was it established immediately after the Battle of Yavin (perhaps partially as a propaganda tool for the Rebellion) or did they think of it later and then retroactively apply it backwards to begin at Yavin? Who knows, I doubt any canonical source addresses the issue. In any case, real world calendars are often conceived of after the fact and then applied retroactively to some past duration of time. Perhaps in retrospect, the Rebels came to believe that the Battle of Yavin was like a “sacred turning point” in their favored historical narrative, and so they chose that as “Year 0”.
Obviously, the real world explanation is that Star Wars 1977 is where it all began. I’ve also seen newer timelines from official Disney material that use Episode 7 and the destruction of Starkiller base as the start of a new dating system or reference point. (bleh…) It’s like the Disney “regime” took some cues from actual dictators and rewrote (fictional) history to center around a new favored cult of personality.