Honestly, there’s not really a good way to do this anonymously without escalating it. You’re within your right to request that it be removed, and you don’t need a solid justification to remove it. I assume it’s just a random promo photo on their instagram? I don’t think they’d care much outside of just removing it.

probably won’t care to comply with my demands

Schools care (or want to appear that they care) about the privacy, safety, and comfort of their students. I think they’d just remove it if asked. You could also try speaking to whoever is running the account and ask them, if say you don’t want to reach out to the admin.

There’s a quick draft:

Hi _______, I saw I was in a recent photo that was posted to the ____ account. I would like to kindly request that the photo be removed, as I value my online privacy and I am trying to have control over where my images are shared. Please let me know if there’s anything else I should do to complete this process, and thank you for your help!

I don’t want to have any sort of direct contact with the school

Then how do you expect it to be taken down. The school posted it, I assume, on an insta account they control.

You first step is to contact them directly and ask for it to be removed.

If you are not willing to do that, which I can understand, I am not sure how you proceed.