docs: clarify CORS motivation and expand backend test descriptions

- Section 5: explain the CORS problem that drove API_BASE='', show
  before/after fetch URLs, document the Vite proxy as the local dev
  equivalent
- Section 6: split into 6.1 (route/integration tests) and 6.2 (unit
  tests), describe what each individual test guarantees about route
  behavior and metric instrumentation

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>