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"Contextuality says that properties of particles, such as their position or polarization, exist only within the context of a measurement"

Does this "surprising" and "less known" fact about quantum mechanics follow from the well-known Heisenberg uncertainity principle, which states effectively that - the more precise the position of a particle is determined, the less precise the momentum can be?

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They are related: The Heisenberg uncertainty principle is a consequence of a more fundamental fact that "measurement operators do not commute", which is the mathematical way of saying "measuring quantity A can result in resetting the expected result from measuring quantity B" (sorry, it is difficult to say something in normal English without it being imprecise). Contextuality is itself a more general way of thinking about non-commuting observables. If anything, I would say that the Heisenberg principle is a consequence of contextuality (but again, this is a vague handwavy statement).

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