🧹 Refactor Github Actions to be more efficient

[e-lo]

Problemo

Right now, the Github Actions take a really long time to run because:

1. There is no caching of libraries.
2. Installs use pip instead of uv (which is implemented in Rust and thus super fast).
3. We don't separate concerns and cache. For example, if the docs push fails, we have to rerun all the tests before we get to the docs.

Solution

1. Cache libraries.
2. Use uv
3. Modularize