One on One with Team Members

Your logic is sound. 15 people is a large team, and there's no way you'll meaningfully interact with all of them over the summer. Prioritize the 1:1 with your intern manager (IM) and the people who will be most important to your project. Four or five 1:1s is a good number in your first week. I talk about this in Onboard Efficiently from the SWE intern course.

Even if you won't work directly with these people, they can (1) expand your network and (2) be helpful in answering generic questions that are agnostic to your particular project. (e.g. "how do I mark this PR comment as resolved?"). So don't view it as wasted time, but don't go overboard by scheduling time with all 15 people.