> What is the gravitational field of a particle in a superposition of two different locations? What about when the superposition collapses? Does the gravity field instantly change shape, faster than light?

This is a symptom of the problem of gravity/spacetime being a handled as a classical field, not really the problem itself. The electromagnetic field for example has this exact same problem, but it's handled by the electromagnetic field being quantized. The problem is that nobody is able to fully quantize gravity.

Not all interpretations of QM have collapses, which tend to be underdescribed even in purely QM terms.