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Yeah that's all fair, I've purposefully cut out a lot of the nuance because it didn't really change my answer. Teaching a student would be very different situation where that kind of precision is necessary.
I disagree with your claim that dark energy doesn't cause the expansion. Applying an acceleration still causes the expansion itself; put dark energy in a static universe and it'll expand, press the accelerator in a car and it'll start driving. Acceleration is a property of motion not a separate entity which causes it; the distinction you're trying to make is semantic at best (is this triple precision now? This is why I don't bother with the minutiae, it's endless lol). The fact it was already expanding is, imho, irrelevant.