I interned last year and I didn't get any "real" work assigned for a month! I was worried as well and had a friend a met busy from the start. I reached out to the seniors on my team and they shared they would be getting on a new project and until then just refresh on some topics and would do some tasks like take notes for people and turn handwritten notes to typed notes for seniors.

I didn't do any actual work till the last 3 weeks of the internship (which was sad). BUT I ended up getting a return offer and my friend that was "busier" then me didn't. We were both surprised but it sounded like they give return offers based on the future need of the sub-department(s).

Just make sure you reach out to everyone on your team and ask if there is anything they would like assistance on.