Good questions to better gauge culture and longterm fit of a startup PE fund?

In the process interviewing with a small fund (5-10 investment/operators) about to raise its first large ($300M+) institutional round. The team is top notch and has a track record investing alongside other top funds in their vertical. They've indicated the new hire would have a longterm path within the firm which is an exciting thing to see looking at what well known firms (top decile returns) the GPs have helped build previously. For the past 3 years I've worked to try and end up in a PE fund investment role focused on execution and portfolio work, which is what this job is being described as since they have their own sourcing engine built already. My current role at a large corp investor is more sourcing focused and little execution, but I know that will change in several more years time. Culture of my small team is great as well, the only complaints I'd have would be to the decentralized bureaucratic structure of the overall corp and below market pay. I'm worried though about falling into "grass is always greener" looking at this opportunity and not appreciating the culture and a solid longterm position I'm in now to go work with a team whose culture I know very little about.

What are questions you would recommend as helpful for gauging the culture of a small team while also showing them that I'm thinking seriously about them for the longterm?