Ambiguous prepositional phrase in a legal document

The question on the form is worded as "Have you enrolled or will soon enroll in health insurance but your health coverage has not started yet?"

This is worded clumsily, for sure. But I think the intention is: "(Have you enrolled or will soon enroll in health insurance) AND your health coverage has not started yet?"

The reason being that if the government department wanted to know if you had health insurance, and then as a follow up question, if your health insurance had started yet or not, this would (should!) have been two seperate questions. That fact that it is written as a single question suggests the emphasis is on whether it has (not) started.

Since the OP has health insurance and it HAS started, I would be inclined to answer "no".

(This is not legal advice and I appreciate you have already sought independent legal advice. But given the nature of the wording, if you answer this question as truthfully and correctly as you can, if it turns out that they actually meant something else, I think you have a safety net - the blame lays squarely with them).