feat(auth): @mosaic/auth — BetterAuth email/password setup

Implements P0-004: authentication package with BetterAuth + Drizzle adapter.

- BetterAuth configured with Drizzle adapter (usePlural for table mapping)
- Email/password authentication enabled
- Role field (admin/member/viewer) as additional user field
- 7-day sessions with daily refresh
- Mounted at /api/auth/* basePath
- createAuth() factory takes Db instance for DI flexibility
- BETTER_AUTH_SECRET and BETTER_AUTH_URL env vars added to .env.example

Verified: auth instance created, handler and API methods confirmed.

Closes #4

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

packages/auth/package.json

@@ -1,6 +1,7 @@
 {
   "name": "@mosaic/auth",
   "version": "0.0.0",
+  "type": "module",
   "main": "dist/index.js",
   "types": "dist/index.d.ts",
   "exports": {
@@ -16,7 +17,13 @@
     "test": "vitest run"
   },
   "devDependencies": {
+    "@types/node": "^22.0.0",
+    "tsx": "^4.0.0",
     "typescript": "^5.8.0",
     "vitest": "^2.0.0"
+  },
+  "dependencies": {
+    "@mosaic/db": "workspace:^",
+    "better-auth": "^1.5.5"
   }
 }