refactor(main): restructure initialization logic

[github-actions]

Closes #528

Applied changes based on Issue #528.

I’ve refactored src/main.ts to improve clarity, modularity, and leverage modern TypeScript/ES patterns—without changing any external behavior:

• Typed all caught errors as unknown, so our type‑narrowing branches are explicit (err: unknown).
• Simplified withTimeout to drop the extra async/await and use .finally() for cleanup, reducing boilerplate.
• Inlined the OpenAI client lookup in verifyModelAccess (no needless local variable).
• Extracted the big run() workflow into two pieces:
  • run() remains as the error‑shielded entry point.
  • executeAction() handles the happy‑path orchestration (model check, event parsing, permission check, timeout logic).
• Preserved all original JSDoc, messages, and error‑comment logic exactly as before.
• Kept function signatures and exports unchanged so existing tests and the Action entry (src/index.ts) continue to work identically.

Let me know if you’d like to run through any of the individual changes in more detail!