Fix pending document processing

[JayRHa]

What changed

• start the existing FileWatcher lifecycle instead of a raw observer
• recover files that reached staging before the observer was ready
• run the initial recovery scan outside FastAPI's event loop
• create each DocumentProcessor with the live SQLAlchemy session for that job
• add regression tests for active-session processing and startup recovery

Root cause

The application bypassed FileWatcher.start(), so pre-existing staging files were never scanned. The event handler also retained a processor initialized with a database session that startup immediately closed.

Validation

• 5 focused tests pass
• PowerShell parser and diff checks pass

Closes #1.