How to get treated like an analyst/grinded over the summer at a firm with "good culture"

Unsure if the title makes sense but I'll explain my situation as much as I can. Also, I am posting here since most internship-related posts are on the IB forum.

After grueling recruiting over a year ago I got a Private Equity internship which I was stoked for. Recently I realized a lot of these PE firms (which used to never take interns or analysts) hire a lot of diversity and nepotism. The DEI presenter during orientation basically insinuated they had quotas and all of the ivy kids on rowing teams that did not even know what their teams have done (deals) or told me their interview process was super easy (mines was not) is why I am saying this. Of course I have no issues with the other interns themselves but I am feeling like maybe the company does not take the interns being here that seriously? It is not rare to see people get MF PE internships freshman or sophomore year and never come back. Also I see now that a MAJORITY of the interns are doing client services/investor relations or some other role that does not actually involve investing. My role is with the actual investing team and I believe they should know that I know my stuff since I did have a fairly difficult interview process... interviewed with ~10 people before the offer, all very technical. Anyways past this tangent.

I was actually looking forward to "grinding it out" this summer at the office doing deals, getting reps in etc. I had a good internship last summer but it was a 40-50 hour work week and most of the work was extremely simple or my capstone/other past cases to show I was learning. I really wanted to get hands-on experience. I know this can be hard to ask for in a 10 week timeframe especially since this is a more serious internship with a lot more $$$ at stake but I want to somehow prove I can step up and do real shit this summer without looking like a cocky kid. Ofc I could go ask my manager once our 1.5 week onboarding ends but I am worried by the fact that we are paid OT and HR said something about trying to keep it at 40 hours although some teams will accept OT work. I do not want to make it seem like I just want to milk to by doing extra work (I know analysts are salaried). At the same time I know of some other interns in IB who make a ton of money over the summer doing OT so that would be a nice plus.

I just do not want to end this summer without doing/learning as much as possible. To be honest I already get very bored at school and have only been challenged doing outside-of-school case studies, the investing club I am in etc... Additionally I have seen other people go into the grinder of some of these top BB or EB internships and coming out with a lot to actually talk about which helps for networking and possibly recruiting FT. ofc I would love this job FT in the case I want to re-recruit (I hope not) it would be great to talk about deals I worked on.

Am I overthinking this or being dumb with what I want? Yes I know it can be viewed as "sad" a 20something year old in college wants to work 80-100 hours during the summer but I've decided to go all in on my career. Looking back (recruiting especially) there are so many things I would change. MAYBE even change where I would have accepted this summer or what I recruited for. I appreciate any input or point of view.