[P1] Share auto-patch logic between `verify --fix` and generation loop

[pro-utkarshM]

Problem

Auto-patching exists only in verify --fix. The generation self-healing loop (#2) needs the same fix-application path. Avoid duplicate logic.

Tasks

• Extract diagnosis→patch application into a reusable function/service (core, not CLI command).
• Call it from both verify --fix and generator phase 3.
• Unit test the shared patcher.

Acceptance

Single code path applies fixes; both entrypoints use it.