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.

frontend/README.md

@@ -0,0 +1,42 @@
+# frontend
+
+This template should help get you started developing with Vue 3 in Vite.
+
+## Recommended IDE Setup
+
+[VS Code](https://code.visualstudio.com/) + [Vue (Official)](https://marketplace.visualstudio.com/items?itemName=Vue.volar) (and disable Vetur).
+
+## Recommended Browser Setup
+
+- Chromium-based browsers (Chrome, Edge, Brave, etc.):
+  - [Vue.js devtools](https://chromewebstore.google.com/detail/vuejs-devtools/nhdogjmejiglipccpnnnanhbledajbpd)
+  - [Turn on Custom Object Formatter in Chrome DevTools](http://bit.ly/object-formatters)
+- Firefox:
+  - [Vue.js devtools](https://addons.mozilla.org/en-US/firefox/addon/vue-js-devtools/)
+  - [Turn on Custom Object Formatter in Firefox DevTools](https://fxdx.dev/firefox-devtools-custom-object-formatters/)
+
+## Type Support for `.vue` Imports in TS
+
+TypeScript cannot handle type information for `.vue` imports by default, so we replace the `tsc` CLI with `vue-tsc` for type checking. In editors, we need [Volar](https://marketplace.visualstudio.com/items?itemName=Vue.volar) to make the TypeScript language service aware of `.vue` types.
+
+## Customize configuration
+
+See [Vite Configuration Reference](https://vite.dev/config/).
+
+## Project Setup
+
+```sh
+pnpm install
+```
+
+### Compile and Hot-Reload for Development
+
+```sh
+pnpm dev
+```
+
+### Type-Check, Compile and Minify for Production
+
+```sh
+pnpm build
+```