Introduce FastAPI backend foundation

[visheshbpatel]

Goal

Introduce FastAPI as the backend foundation for SynapseAI.

Tasks

• Create FastAPI application entry point
• Create initial API structure
• Add health endpoint
• Add centralized configuration
• Document the initial architecture

Notes

This begins Phase 3 of the SynapseAI roadmap.

The architecture should remain extensible for future:

• authentication
• multi-user support
• conversations
• document ownership
• additional API features