Correctness defined as "this produces the right answer" vs correctness defined as the above with the addition of "this does not leak information / is not highly vulnerable to side-channel attacks" are very different things, and only one of those definitions is actually useful for cryptography.

Writing it yourself for the first time, or just copying some code off the internet, is going to have a vanishingly small chance of being actually secure.

Totally agree with the sentiment of your statement, but RSA is probably a terrible choice, especially if you want to get it done in 20 lines of code. This article explains it pretty well: https://blog.trailofbits.com/2019/07/08/fuck-rsa/