I don't believe your description is accurate. The primaries are the election that chooses the candidate, these are not open. During the primaries, the presidential preference election, you are given the ballot of your registered party, unless you are registered independent, non-partisan, or an unrecognized party, in which case you can choose from among Green, Republican, Democrat, or Libertarian. Once you do, you can't exchange. If you are registered R, G, or L, you will be given the corresponding ballot, so you will need to reregister. The general election is the election for president, and this is the open one, where you can vote for Yang even if you're registered R, G, or L (if he's elected in the primary to be D candidate).

Again,

"Primary" = "Presidential Preference Election" = first election, picks the candidate for the democrats, closed, but you can change your affiliation before the deadline to vote in the dem primary for yang.

"General Election" = second election, picks the person Arizona's delegates vote for in the electoral college, open, and anyone can vote for anyone.