Platform recommendation for an online competitive programming school
My first instinct is that any LMS is overkill.  LMSs manage classrooms, it's true, but they also are designed to help manage schools, and most of the administrative end (and most of the features outside of the literal classroom aspects, and even many of the features within the classrooms) of any LMS would be completely useless to you.  Busing, medical designations, learning disability plans, school lunch designations, guidance counselor assignments, etc, etc, etc, etc, etc, are all beyond what you need for such a small program.
I'm assuming that most of what you're looking for is a way to distribute and receive assignments.  If this is, indeed, the case, I actually recommend using GitHub.
At the start, kids can simply use your repo as a way to download files through the web interface, and can submit early assignments through Discord, just as you've already done.  After they're comfortable with the GitHub interface for downloading, you can start having them fork projects.  Introduce git functionality slowly, and keep supporting them with Discord in the meantime.
You'll get two big big benefits out of this approach:

You don't have to get into anything nearly as heavyweight as an LMS.
The students will slowly become familiar and comfortable with basic git actions.