feat: scaffold FastAPI backend and Vue 3 frontend

Backend (backend/):
- FastAPI app with layered app/{api,core,crud,db,models,schemas} structure
- TiDB connection via SQLAlchemy. The URL is built with URL.create rather
  than string formatting: the password contains '@', which would otherwise be
  parsed as the user/host separator and silently truncate the credential.
- Alembic environment wired to Base.metadata and the app settings, so
  backend/.env stays the single source of truth for credentials
- /api/health endpoint reporting database reachability
- models/ and crud/ are intentionally empty: no model classes are defined and
  no tables are created, at import time or otherwise

Frontend (frontend/):
- Vue 3 + Vite + TypeScript scaffold (create-vue, --bare)
- axios instance with a normalized error shape
- vue-router with a home route and a catch-all 404
- pinia + pinia-plugin-persistedstate; the app store persists selected keys
- Element Plus with its icons registered globally
- dev proxy forwards /api to the FastAPI service on port 8000

The database paper_doc was created in TiDB out of band; no table exists yet.

backend/app/models/__init__.py

@@ -0,0 +1,15 @@
+"""SQLAlchemy ORM models.
+
+This package is intentionally empty.
+
+No model classes exist yet, and no tables are created by this project at
+import time. The schema will be introduced through Alembic migrations:
+
+    alembic revision --autogenerate -m "describe the change"
+    alembic upgrade head
+
+When the first model is written, add it here (or in a submodule imported from
+here) so that ``Base.metadata`` — and therefore autogenerate — can see it.
+"""
+
+__all__: list[str] = []