So usually this is explained with two scientists, Alice and Bob, on far away planets. They’re each in the possession of a particle that is entangled with the other, and in a superposition of state 1 and state 2.

This "usual" way of explaining it is just overly complicating it and making it seem more mystical than it actually is. We should not say the particles are "in a superposition" as if this describes the current state of the particle. The superposition notation should be interpreted as merely a list of probability amplitudes predicting the different likelihoods of observing different states of the system in the future.

It is sort of like if you flip a coin, while it's in the air, you can say there is a 50% chance it will land heads and a 50% chance it will land tails. This is not a description of the coin in the present as if the coin is in some smeared out state of 50% landed heads and 50% landed tails. It has not landed at all yet!

Unlike classical physics, quantum physics is fundamentally random, so you can only predict events probabilistically, but one should not conflate the prediction of a future event to the description of the present state of the system. The superposition notation is only writing down probability amplitudes of the likelihoods of what you will observe (state 1 or state 2) of the particles in the future event that you go to the interact with it and is not a description of the state of the particles in the present.

When Alice measures the state of her particle, it collapses into one of the states, say state 1. When Bob measures the state of his particle immediately after, before any particle travelling at light speed could get there, it will also be in state 1 (assuming they were entangled in such a way that the state will be the same).

This mistreatment of the mathematical notation as a description of the present state of the system also leads to confusing language like "it collapses into one of the states" as if the change in a probability distribution represents a physical change to the system. The mental picture people say this often have is that the particle literally physically becomes the probability distribution prior to measuring it---the particle "spreads out" like a wave according to the probability amplitudes of the state vector---and when you measure the particle, this allows you to update the probabilities, and so they must interpret this as the wave physically contracting into an eigenvalue---it "collapses" like a house of cards.

But this is, again, overcomplicating things. The particle never spreads out like a wave and it never "collapses" back into a particle. The mathematical notation is just a way of capturing the likelihoods of the particle showing up in one state or the other, and when you measure what state it actually shows up in, then you can update your probabilities accordingly. For example, if you the coin is 50%/50% heads/tails and you observe it land on tails, you can update the probabilities to 0%/100% heads/tails because you know it landed on tails and not heads. Nothing "collapsed": you're just observing the actual outcome of the event you were predicting and updating your statistics accordingly.