If the question feels unclear to you, that’s an excellent opportunity to ask clarifying questions, e.g. “Sure, but what do you mean by ‘conflict’? Do you mean a disagreement on how to solve a problem, or an interpersonal conflict?”
When I ask a question like this I mean a disagreement, and I’d imagine that’s what most interviewers mean too. So I recommend you continue to search for a situation you can recall in detail.
If the answer is that they’re looking for interpersonal conflict, you should use a situation where you took effort to work past it with the person for the good of the mission/company. Your last story could work if framed that way but it lacks a moment where you found a way to move forward with this person.