Implementing an HTTP server from scratch in C is quite simple, clients are harder though, so I would keep using libcurl.
HTTPS can be tricky though, so you probably want to delegate this part to a reverse proxy.
Implementing an HTTP server is easy, but implementing a fast, feature-complete and secure one is complex.
What you gain by rolling your own instead of using a battle tested solution is a reduced attack surface. For example, an off-the-shelf HTTP server may be tricked into revealing the content of a file the user should not have access to, but if your custom server doesn't read files at all (you don't even make a open()) because everything is in RAM, or hardcoded in the executable itself, then such a vulnerability cannot exist. You may also decide to allocate most of your memory statically, because you know in advance how much you will need, and doing that, eliminate an entire class of potential vulnerabilities. An off-the-shelf HTTP server doesn't have this luxury.
And with one less dependency, you are also less vulnerable to supply chain attacks.