feat: improve apply_code tool with isolated API context for diff generation

- Create truly isolated API handler for Stage 2 diff generation
- Use hardcoded, optimized system prompt for diff generation
- Ensure clean context without conversational history in Stage 2
- Update tests to reflect the new implementation

This addresses the subtle but important difference pointed out by @CberYellowstone
in issue #6159, where the original proposal emphasized creating a truly isolated,
dedicated process for diff generation.

Author: roomote