TCP has been around a long time. Listen, read, send, you're good to go. It's just software so you can make it do anything.

But you're asking about the relationship between popular primarily file serving servers like Apache and their relationship to high level code to create custom responses? Yeah, CGI was the first big standard there that I remember, though it was a bit before my time. But that's only one possible architecture.

These days, most web apps have the web server built in, and so the custom code you're writing works with the full request directly. There may be a lightweight web server in front (or multiple), like nginx, to manage connections, but they will largely just proxy the whole thing through.