refactor: split rig providers into own crate

- [x] I have looked for existing issues (including closed) about this

## Feature Request

The title is self explanatory.

### Motivation

The rationale behind this is that if we split the providers into its own crate, users are then able to essentially use whatever providers they want without anything else.

I think this is important because it does seem that Rust is missing a good crate just for calling LLMs.

### Proposal

Split the `rig::providers` module into its own crate. That's pretty much it.

### Additional
I will be assigning this work to myself as this is a very large change with sweeping implications if this gets accepted.

The providers module is currently in rig::providers. Examine its structure, dependencies, and how it's used throughout the codebase. The goal is to extract it into a separate crate, which involves updating Cargo.toml, managing public/private APIs, and ensuring downstream usage remains compatible. Start by reviewing the existing module and its integration points.

索引モデルが issue の本文から書いたものです。