Normally during a project, I tend to restructure the code quite a bit.
First when it is small, I do it like you and have everything in one file, then as it grows I start to split out the things in to multiple files/modules. Then as it grows even further, I create subfolders. Try to define parts of the algorithms and break them out to their own modules. Like if you have a scheduling part, then you move that to scheduler.rs. Also, move out special types to types.rs, error types to errors.rs to keep the area with the actual algorithms more clear.
So, that the code feels like a mess as it grows is just a normal thing. And often, it is not worth trying to plan that much ahead since it is very difficult to predict the needs.
But for a REST server I have something like this
src/main.rs
src/types.rs
src/api/v1/mod.rs
src/api/v1/errors.rs
src/api/v2/mod.rs
src/api/v2/errors.rs
src/api/v2/types.rs
src/tests/v1.rs
src/tests/v2.rs
But the before the v2 version of the api, there was just a src/api.rs, src/errors.rs . So, I think the key is to not be afrad to shuffle code around and restructure it as you need. And it will not always be good, but then you just do it again. One of the things with a very strict language like Rust is that you can shuffle it around, and rewrite it without a big risk of adding hidden bugs.