refactor(api): convert Depends(get_db) to db: Any = None across API endpoints to release connection pool early

[yaojin3616]

Summary of Changes

• Connection Pool Optimization & Disentanglement: Refactored long-lived db: AsyncSession = Depends(get_db) FastAPI parameter injections across 35 API endpoint files to optional db: Any = None.
• Prevent Connection Starvation: By disentangling Request-level DB session allocation from the API routes, DB connections are no longer held alive for the entire duration of HTTP requests (which may involve long-running LLM inferences, streaming, or external RPCs). Connections are now acquired on-demand within narrow DAO calls and released immediately back to the pool.
• Backward & Unit Test Compatibility: Preserves optional db: Any = None parameter for Unit Tests mocking and explicit session passing.
• Verification: All 2141 unit tests passed cleanly and scripts/arch-guard.sh constitutional check passed.