feat: add FastAPI backend with PostgreSQL and start script fixes

- Add server/ directory with FastAPI backend
- Fix server/start.sh to properly handle venv on Windows/Git Bash
- Add alembic migrations and pyproject.toml
- Add server tests

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

server/src/app/api/router.py

@@ -0,0 +1,6 @@
+from fastapi import APIRouter
+
+from app.api.v1.router import router as v1_router
+
+api_router = APIRouter()
+api_router.include_router(v1_router)