feat(api): integrate Better Auth with Drizzle adapter and social providers

- Add Better Auth config with Google + GitHub social providers
- Mount auth handler on /api/auth/* in Express
- Generate and migrate auth tables (user, session, account, verification)
- Deduplicate term_glosses data for tighter unique constraint
- Drop legacy users table

apps/api/src/app.ts

@@ -1,11 +1,14 @@
 import express from "express";
 import type { Express } from "express";
+import { toNodeHandler } from "better-auth/node";
+import { auth } from "./lib/auth.js";
 import { apiRouter } from "./routes/apiRouter.js";
 import { errorHandler } from "./middleware/errorHandler.js";
 
 export function createApp() {
   const app: Express = express();
 
+  app.all("/api/auth/*splat", toNodeHandler(auth));
   app.use(express.json());
   app.use("/api/v1", apiRouter);
   app.use(errorHandler);