You don’t need to use codepen, but if you use codepen you need an account. With a free account on codepen you can create as many pens as you want which is what you need for the projects.
Just to clarify, codepen has what are called projects and pens.
What everyone is talking about are the unlimited pens with the free account.
For the freeCodeCamp projects you can just use the free account with the pens.
Codepen also has what they call projects which allow for multiple HTML, CSS and JavaScript files.
You are only allowed one codepen project with the free account.
But for your purposes you just need to create pens and it is always free.
This is where you can find the free pens.