I got rejected at a mid-sized tech company with ~2000 employees for a security engineering internship after the final round about 1 and a half months ago, but the recruiter said to keep in touch for future opportunities at the firm and also voluntarily gave me feedback in the interview process.
She gave me the biggest reason I was rejected was because there weren't any projects available that fit me at the time. I also have my hiring manager's email as well from the final round interview and he told me at the end of the interview to keep in touch.
Should I reach back out to the recruiter and/or hiring manager to check up on their projects and ask for a potential internship in the Fall or Winter? If so, what should I say in the email?