How do I implement a plagiarism detector completely from scratch and it has to be fast as well?

If you are going to check for copy-pasted things, algorithms for text-comparison would be ok, just extract the amount of differences between a paragraph and what you crawled to your DB and set a contingency percentile to spot something as plagiarism.
If you want better performance spot keywords to index, make an in-memory DB copy (if it suits your budget) and so on, pretty standard.

I remember reading something about that involving ML but that's a bit tricky because there's a limited amount of ways you can explain something.

I.e. There's a limited amount of synonyms for a word, there's a limited amount of meanings for an idiom, a word and so on.

Then each discipline has it's own flexibility; you can explain in more ways how gravity works than the amount of ways you can think of while explaining a cooking recipe step by step.

That's to say that training an AI to correctly spot plagiarism without reporting falsy positives is pretty hard.

Hope it helps somehow

Nah, it is a hobby project. Our school won't give anything interesting to do🥲

I have that in a database based on many web pages

I start by learning Pascal, then write some code in C++, and to finish, I'd made something that works in JS.

Feel free to copy my comment.