How should a high-school student approach professors in research institutions about research opportunities?
It might be better, if you can arrange it, to have one of your teachers help you with this. It may well be that one of your STEM teachers went to one of these universities, or has some contact there. If so, they can help you make contact, vouch for your seriousness, and ease the way.
This is much harder now in the pandemic, but perhaps it can be arranged in virtual space. A phone call from a teacher to a professor before you make contact will make all the difference. Even if none of your teachers have any contacts, a mail from them, introducing an &quot;interesting student&quot; will make your contact much more likely to bear fruit. Make sure that your teacher can say some interesting things about you and your interests and skills.
This should avoid the &quot;bulk&quot; problem and you can approach it one step at a time.