How much background do I need for Kingdom Hearts 3?

I've played Kingdom Hearts, and the numbered sequel Kingdom Hearts 2. I'm aware that other games in the series exist, but I haven't played them. Now I'm trying to start Kingdom Hearts 3 and having a bit of trouble getting into it, because there seems to be a bunch of story I'm missing somewhere. Just from the very beginning of the game:

• Apparently Sora recently took some sort of important test and failed it.
• There's someone important out there named Aqua who I have never heard of, that Riku and Mickey are looking for.
• There's someone important named Terra who's connected to Aqua, who, despite what you might assume given the series's Final Fantasy connections, is definitely not Terra from FF6 because this one's a man!
• Kairi is off with Axel (who's a good guy now and is called Lea) doing... some sort of training somewhere?

What in the world is going on here?!? You generally sort of assume that numbered entries in a series are the core story of the series, and non-numbered entries are spinoffs that aren't particularly relevant to the main series's storyline, but it appears that this is not a safe assumption in this case!

A bit of Googling suggests there are around a dozen "spinoff" games I've never played. Which ones of them are part of the main continuity that I need to be familiar with in order to pick up Kingdom Hearts 3 and understand what's going on?