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>

src/components/auth/forgot-password-form.tsx

@@ -0,0 +1,83 @@
+"use client"
+
+import { useState } from "react"
+import Link from "next/link"
+import { Button } from "@/components/ui/button"
+import { Input } from "@/components/ui/input"
+import { Label } from "@/components/ui/label"
+import { requestPasswordReset } from "@/lib/auth-client"
+
+export function ForgotPasswordForm() {
+  const [email, setEmail] = useState("")
+  const [error, setError] = useState("")
+  const [success, setSuccess] = useState(false)
+  const [isPending, setIsPending] = useState(false)
+
+  const handleSubmit = async (e: React.FormEvent) => {
+    e.preventDefault()
+    setError("")
+    setIsPending(true)
+
+    try {
+      const result = await requestPasswordReset({
+        email,
+        redirectTo: "/reset-password",
+      })
+
+      if (result.error) {
+        setError(result.error.message || "Failed to send reset email")
+      } else {
+        setSuccess(true)
+      }
+    } catch {
+      setError("An unexpected error occurred")
+    } finally {
+      setIsPending(false)
+    }
+  }
+
+  if (success) {
+    return (
+      <div className="space-y-4 w-full max-w-sm text-center">
+        <p className="text-sm text-muted-foreground">
+          If an account exists with that email, a password reset link has been sent.
+          Check your terminal for the reset URL.
+        </p>
+        <Link href="/login">
+          <Button variant="outline" className="w-full">
+            Back to sign in
+          </Button>
+        </Link>
+      </div>
+    )
+  }
+
+  return (
+    <form onSubmit={handleSubmit} className="space-y-4 w-full max-w-sm">
+      <div className="space-y-2">
+        <Label htmlFor="email">Email</Label>
+        <Input
+          id="email"
+          type="email"
+          placeholder="you@example.com"
+          value={email}
+          onChange={(e) => setEmail(e.target.value)}
+          required
+          disabled={isPending}
+        />
+      </div>
+      {error && (
+        <p className="text-sm text-destructive">{error}</p>
+      )}
+      <Button type="submit" className="w-full" disabled={isPending}>
+        {isPending ? "Sending..." : "Send reset link"}
+      </Button>
+      <div className="text-center text-sm text-muted-foreground">
+        Remember your password?{" "}
+        <Link href="/login" className="text-primary hover:underline">
+          Sign in
+        </Link>
+      </div>
+    </form>
+  )
+}