feat: implement password reset API endpoint and wire up form

- Add POST /api/auth/password-reset endpoint to validate email and process reset requests
- Wire up password reset form to call API instead of stubbing success
- This enables proper password reset flow for Issue #10

src/app/auth/password-reset/page.tsx

@@ -15,6 +15,22 @@ export default function PasswordResetPage() {
     setError("")
 
     try {
+      const response = await fetch("/api/auth/password-reset", {
+        method: "POST",
+        headers: {
+          "Content-Type": "application/json",
+        },
+        body: JSON.stringify({ email }),
+      })
+
+      const data = await response.json()
+
+      if (!response.ok) {
+        setError(data.error || "Failed to send reset link")
+        setLoading(false)
+        return
+      }
+
       setSent(true)
     } catch (err) {
       console.error("Password reset error:", err)