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/deps.py

@@ -0,0 +1,13 @@
+from collections.abc import Generator
+
+from sqlalchemy.orm import Session
+
+from app.db.session import get_session_factory
+
+
+def get_db() -> Generator[Session, None, None]:
+    db = get_session_factory()()
+    try:
+        yield db
+    finally:
+        db.close()