I like your approach, mostly because it's bottom-up, and because this is an excellent opportunity to illustrate common pitfalls. Those pitfalls can be identified using sanitizers (-fsanitize=undefined,leak,address,thread etc). With the correct CI setup you'll have a safety net, where sanitizers provide precise motivations why one approach works, and another also works, but at risk of undefined behaviour.

I have no opinion on use of C89 instead of C++, since that's just an implementation detail. Also, for your purposes, it works to your advantage, since C is basically the white-box of C++.