It's not that handmade projects shouldn't ever use libraries - it's more that you should be conscious of everything your program is doing, cut away unnecessary abstraction, and focus on performance and elegance. Also, it's really tough to do web stuff "properly" without the use of libraries, especially if you want to handle newer technologies like HTTP/2.
I'm not familiar with server options in C, but if you're looking for a C-like option that isn't as bloated as a Java app, I would recommend looking into
Go. Go itself is a compiled language with a lot of similarities to C (although it is garbage-collected), and the
http package in Go's standard library makes it easy to get a basic HTTP server up and running, without prescribing much else.
If you are used to bigger web frameworks and want features like middleware functions, you could also use a simple framework like
Gin, which gives you a more conventional framework structure but is still nowhere near as bloated as your average Java framework.