Improve PDF-to-Lean Proof Translation Pipeline (SKILL)

[kencyke]

I’d like to refactor and improve the SKILL code introduced in #12.
Ideally, I’d like to extract the SKILL code into a standalone package that can be shared on GitHub.

cf.

• https://github.com/facebookresearch/repoprover
• https://github.blog/changelog/2026-04-16-manage-agent-skills-with-github-cli/
• https://github.com/AxiomMath/axle-mcp-server
• https://github.com/rjwalters/lean-genius
• https://github.com/forrestchang/andrej-karpathy-skills