refactor(proxy): clean up integration test naming and style

- Remove '// ---------- Integration Tests ----------' section separator
- Rename 'hdr'/'Hdr' variables to 'header'/'Header' for clarity
- Rename 'llm'/'llmBackend' to 'injectBackend'/'inject'/'backend'
  to reflect the actual concept (inject target) rather than a
  specific use case (LLM)
- Update comments to match the new naming

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Author: SasSwart