Can't seem to find a clear answer on this. Does the N64 version of Banjo-Kazooie autosave?

Save slot 2 and 3 were already used for my own playthrough and were further than we got that day. I don't understand what you're implying but you're incorrect either way.

I don't think games from that era really had an auto save feature, and if they did you would want to save whenever you could if given the option anyways because that feature was very inconsistent from game to game.

Yes it autosaves. This is the reason why the original only saved note scores, so it didn't have to save after each individual note, only when you left the level.

Interestingly the manual showed a "save and continue playing" option in its screenshot of the menu so manual saving was obviously planned at some point.