Migrate authentication from next-auth to Better Auth

[theNEXlevel]

Summary

Replaces next-auth (Auth.js v5 beta) with Better Auth, keeping the existing Google sign-in and adding email/password login with new /signin and /signup pages.

Server

• src/lib/auth.ts is now a betterAuth instance (Prisma adapter, Google provider, email/password enabled); a getSession() helper replaces auth() in all API routes and server pages with the same session.user.{id,role} shape
• Admin impersonation is preserved — the cookie-override logic moved from the next-auth session callback into a customSession plugin
• Handler moved from /api/auth/[...nextauth] to /api/auth/[...all]

Client

• src/lib/auth-client.ts (better-auth/react) replaces next-auth/react; SessionProvider removed from the root layout; session update() calls became refetch()
• User menu "Sign In" routes to the new /signin page

Database

• Schema rebuilt for Better Auth: boolean emailVerified, required name, new Account/Session shapes, Verification replaces VerificationToken
• Hand-written migration carries over existing Google account links; active sessions are dropped (users sign in again). Google is a trusted linking provider as a fallback
• Seed rewritten without @auth/prisma-adapter

Config

• NEXTAUTH_URL → BETTER_AUTH_URL (example.env, docker-compose, Dockerfile); AUTH_TRUST_HOST dropped
• AUTH_SECRET, AUTH_GOOGLE_ID, AUTH_GOOGLE_SECRET unchanged, so existing CI secrets keep working; the Google OAuth callback path is identical (no GCP console changes)

Test plan

• pnpm build, pnpm test (45 tests), pnpm lint, tsc --noEmit all pass
• Migration applied cleanly to a database containing existing next-auth data; seed runs
• Live-verified against the running app: email/password signup, sign-in (and wrong-password rejection), session includes role, /dashboard gating (200 with session, 307 anonymous), sign-out, and Google authorization URL generation
• Google sign-in completed in a browser (needs interactive login)
• Impersonation exercised by an admin (logic ported 1:1, typechecked, not live-tested)

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