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/alembic.ini

@@ -0,0 +1,45 @@
+[alembic]
+script_location = alembic
+prepend_sys_path = .
+path_separator = os
+version_path_separator = os
+
+# The database URL is deliberately NOT set here. It is resolved at runtime by
+# alembic/env.py from the application settings (backend/.env), so that there is
+# exactly one source of truth and no credential is stored in a tracked file.
+
+[post_write_hooks]
+
+[loggers]
+keys = root,sqlalchemy,alembic
+
+[handlers]
+keys = console
+
+[formatters]
+keys = generic
+
+[logger_root]
+level = WARNING
+handlers = console
+qualname =
+
+[logger_sqlalchemy]
+level = WARNING
+handlers =
+qualname = sqlalchemy.engine
+
+[logger_alembic]
+level = INFO
+handlers =
+qualname = alembic
+
+[handler_console]
+class = StreamHandler
+args = (sys.stderr,)
+level = NOTSET
+formatter = generic
+
+[formatter_generic]
+format = %(levelname)-5.5s [%(name)s] %(message)s
+datefmt = %H:%M:%S