But collapse is fake news, as it were. A state can be called a “superposition” only relative to a particular set of basis states, which, in turn, depends on what observable we are talking about, and the “collapse” is simply yet another way a state can change.

No, collapse or some alternative to it is a fundamental component of quantum mechanics. Without it, quantum mechanics makes wildly wrong predictions.

The Schrodinger equation almost always predicts that a particle has some particular amplitude at many different locations. However, if you try to detect a particle, you will never find it at more than one location. Furthermore, once the particle is detected at one particular location, you need to update the Schrodinger equation to give it amplitude 1 at that location and 0 everywhere else - if you don't perform this nonlinear update and instead use the old wave-function, the predictions for further experiments will be completely off.

Now, the physical interpretation of this collapse varies wildly between different interpretations of QM, but some variant of it is always required - otherwise, the observations simply do not match the math. We don't yet have any theory consistent with QM that can make predictions without applying the Born rule.

I believe in Many-Worlds, the update step falls out of decoherence "for free." Because you are also in superposition after the measurement, the "you have measured 1" part of your wavefunction of course measures amplitude 1. That doesn't give you the Born rule though - I believe there's some attempts to get it out of game theory [1], where they show that given sufficiently long timespans, "almost every" worldline has a history with quantum measurements whose distribution matches the Born probabilities.

[1] https://arxiv.org/abs/0906.2718