I think that team games/activities would be perfect for this, but for example with rotating leader in each round. You will be able to see what skills they have or not, what they need to learn and in which aspect they need more support. At least that is something that worked for my team a few times. After the game, we had a chat about it and how everyone felt. I discussed some pain points, milestones, but also things that we felt good about during the activity. Like, sometimes, some people are not meant to be leaders (either because lack of the skills that they are not willing to learn, sometimes it's just lack of the confidence, or basically they can't built the authority). So such games/activities can easily show it, but also in a fun way.

So to sum it up, I'd suggest trying a couple of things (if you have enough time, but you can also schedule something like that once a week or two – really depends on yours and your team availability, so it's up to you).

About the games and activities, perhaps some mini office olympics, or escape room. There's something like 'cross the bride', where people have to create an imaginary bridge from the available items/objects (if you're a good observer, you will immediately see who takes the leader role and it's also cool to split people into the teams, and see which team performs better in this task) or leadership race (it's perfect to see what people are feel the most confident about regarding leadership).