Is it true that test engineer internships typically pigeon hole you into a software testing career?

Some background: My goal is to become a SWE, so I applied to a broader "IT" internship posting at this company, but after acceptance, they put me into the manual testing position.

I had initially applied to 600 internships (with only 5 interviews) before finally getting this one, and I feel like I might need to struggle a lot to get a different internship. I have no "official" SWE experience. Here are my stats: I have an unpaid and unofficial computer vision research experience, a CRUD web app project, a hackathon win, and another unpaid and unofficial product management internship at a startup (I only got it because the CTO was someone I knew at my school).

With my stats and my goal of becoming a SWE, can someone advise me whether I should take the manual testing internship, or should I try to go for another internship, knowing I'm going to spend time doing LeetCode, researching companies, and interviewing instead of studying for finals?