[Feature] Introduce mypy in a gradual rollout way

[guo-han]

Checklist

• 1. If the issue you raised is not a feature but a question, please raise a discussion at https://github.com/sgl-project/sgl-jax/discussions/new/choose Otherwise, it will be closed.
• 2. Please use English, otherwise it will be closed.

Motivation

Introduce mypy into codebase (in pre-commit maybe) would help catch low-level bugs early, like previously done in vllm, jax, etc.
Follow a gradual rollout plan to achieve this.

Related resources

https://docs.jax.dev/en/latest/jep/12049-type-annotations.html
https://github.com/vllm-project/vllm/pull/25313/files#diff-6b980d504c08a48078accc6b5fb392b7b5d4c65dfe293a3956a7109200f184e2

[JamesBrianD]

Nice job — this looks great!
If possible, could you also help add a bit more detail in two areas?

• Mypy config suggestions — e.g., recommended mypy.ini options.
• Gradual rollout plan — a rough outline of how we expand the coverage step by step (e.g., start with /models, then /layers, later tighten the rules).

I’d also be happy to help coordinate or assist with the rollout, so feel free to loop me in on anything you need. Thanks!