Is it fine to ask this kind of question to the corresponding author of a paper?

Your advisor will give the best advice, of course, especially if he knows any of the people involved. But in general there is no ethical reason you can't ask such questions of an author.

But I might phrase it differently. I'd probably ask if there is any current work on the topic that will shed more light on the questions. And your suggestion of asking if they think it is a good line to pursue is good also, I think. Express your interest in the topic and that you are considering it as a research topic.

But I wouldn't couch the question in terms of responding directly to a (partial) rebuttal if that's how you judge the new work. It doesn't sound like that is the case, though, so just asking about what they can tell you about current thinking and research is fine.

And, if they are working on the topic it might save you from the problem of going along on a parallel track and getting scooped by more experienced researchers.

Take your advisor's advice, but from what you've said here it sounds like a perfectly reasonable question.

quite renowned researcher, briefly disputing the claims made in the first paper.

The fact that there is disagreement only proves that the topic as a worth investigating. In other PhDs, you have to prove that the topic is worth investigating. With this topic, you would need to develop convincing methodologies to explore the area of contention and delineate the nuances of the controversy. Expert would not have the time to do all that tedious work.

Contacting experts may not really help in this circumstance. Opinions are not as important as evidence. Experts disagree all the time, and they are allowed to change their mind whenever, so pressuring them for an opinion seems a waste of your time. Experts might change their mind right after your discussion, it is their prerogative.

It could be that both experts were right but you proved that it really depends on the differences in the initial circumstance. However, you might have to be quick as Buffy suggests, if two experts are clashing, there will likely be more experienced researchers scooping up the interest pronto. So a quick publishing strategy would be better than a long form approach.