feat: replace Google OAuth with email/password authentication

Replace Google OAuth provider with email/password authentication to reduce
friction for MVP development and vibe coding workflows.

Changes:
- Remove Google OAuth configuration from auth.ts
- Add emailAndPassword provider with enabled: true
- Add email verification with sendOnSignUp: true
- Add password reset functionality
- Log verification and reset URLs to terminal (no email integration yet)

New auth pages (src/app/(auth)/):
- /login - Sign in page
- /register - Sign up page
- /forgot-password - Password reset request
- /reset-password - Password reset completion

New components (src/components/auth/):
- sign-up-form.tsx - Registration form
- forgot-password-form.tsx - Password reset request form
- reset-password-form.tsx - Password reset form

Updated components:
- sign-in-button.tsx - Now email/password form instead of Google button
- user-profile.tsx - Shows Sign in/Sign up buttons when logged out

Bug fixes:
- Fix React render error in profile page by wrapping router.push in useEffect

Config updates:
- Remove GOOGLE_CLIENT_ID and GOOGLE_CLIENT_SECRET from env.example
- Update CLAUDE.md documentation to reflect email/password auth
- Add requestPasswordReset, resetPassword, sendVerificationEmail to auth-client exports

All changes applied to both main project and create-agentic-app template.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

CLAUDE.md

@@ -8,7 +8,7 @@ This is a Next.js 16 boilerplate for building AI-powered applications with authe
 
 - **Framework**: Next.js 16 with App Router, React 19, TypeScript
 - **AI Integration**: Vercel AI SDK 5 + OpenRouter (access to 100+ AI models)
-- **Authentication**: BetterAuth with Google OAuth
+- **Authentication**: BetterAuth with Email/Password
 - **Database**: PostgreSQL with Drizzle ORM
 - **UI**: shadcn/ui components with Tailwind CSS 4
 - **Styling**: Tailwind CSS with dark mode support (next-themes)
@@ -34,6 +34,11 @@ This is a Next.js 16 boilerplate for building AI-powered applications with authe
 ```
 src/
 ├── app/                          # Next.js App Router
+│   ├── (auth)/                  # Auth route group
+│   │   ├── login/               # Login page
+│   │   ├── register/            # Registration page
+│   │   ├── forgot-password/     # Forgot password page
+│   │   └── reset-password/      # Reset password page
 │   ├── api/
 │   │   ├── auth/[...all]/       # Better Auth catch-all route
 │   │   ├── chat/route.ts        # AI chat endpoint (OpenRouter)
@@ -45,7 +50,10 @@ src/
 │   └── layout.tsx               # Root layout
 ├── components/
 │   ├── auth/                    # Authentication components
-│   │   ├── sign-in-button.tsx
+│   │   ├── sign-in-button.tsx   # Sign in form
+│   │   ├── sign-up-form.tsx     # Sign up form
+│   │   ├── forgot-password-form.tsx
+│   │   ├── reset-password-form.tsx
 │   │   ├── sign-out-button.tsx
 │   │   └── user-profile.tsx
 │   ├── ui/                      # shadcn/ui components
@@ -83,10 +91,6 @@ POSTGRES_URL=postgresql://user:password@localhost:5432/db_name
 # Better Auth
 BETTER_AUTH_SECRET=32-char-random-string
 
-# Google OAuth
-GOOGLE_CLIENT_ID=your-google-client-id
-GOOGLE_CLIENT_SECRET=your-google-client-secret
-
 # AI via OpenRouter
 OPENROUTER_API_KEY=sk-or-v1-your-key
 OPENROUTER_MODEL=openai/gpt-5-mini  # or any model from openrouter.ai/models