Any time you apply for a driver’s license or whatever, you are asked if you want to register with a party. That is the party that you will vote for in the primary elections. Some (many?) states offer same day registration which, in my opinion, is how it should be. It puts you in a database in case voter fraud ACTUALLY happens (insanely rare) where they can check to make sure Ur Quell only voted once and investigate what happened if they see multiple votes.

As for the primaries: This is how the US handles our version of Ranked Choice and… I kind of prefer it (with some major caveats). The general idea is that all right wing politicians should run for the republican seat and all sane people for the Democrat seat. You campaign at the tail end of the previous year and the party members vote on you in the spring. There is definitely some sketchiness with super delegates (although, that is not overly dissimilar from how many parliament systems pick a Prime Minister), but this creates a unified front come November.

Yes, two party systems are bad, but that is what things tend to converge on when push comes to shove. Just look at France where the Left more or less unified to stand a chance against fascism.

Like almost every aspect of the US government: it is a fundamentally good system that needs to be iterated on and better taught to the populace. It is just that republicans know that education hurts them and want to take advantage of all the loopholes that Tommy Jefferson obviously intentionally wrote while he was raping his plantation full of slaves.