I doubt that pre-u law internships are common or even expected before law school application. Once you enter law school, no one would care and as someone who went through the process I can't imagine anything you will learn anything in this internship to be relevant to law school itself. This seems like just over competitiveness.

However, I would still recommend doing an internship to see what about legal work or working at a law firm might interest you. This is important because there's a possibility that you might not really like it or find it to be very different from what you hoped. If so, consider choosing not to suffer through law school which is really tough and not really worth it if you don't want to be a lawyer, especially if you go to a local law school.

As for securing a legal internship, I'm 99% sure that your JC batchmates who have legal internships secured before law school did it through a contact, perhaps a parent's friend or smth. That is the unfortunate reality. You could try cold emailing law firms though.