feat(auth): finish Turnstile coverage across every auth entry point

Turnstile protected sign-in, sign-up and password-reset, but three gaps
remained:

- updatePassword had no verification and its page had no widget, so the
  final step of the reset flow was unprotected. The reset token is now
  carried through the failure redirect so a failed challenge doesn't
  strand the user on a form whose emailed link can't be replayed.

- /api/auth/[...all] exposed better-auth's handler directly, accepting
  unlimited credential guesses and email sends with no bot protection --
  a full bypass of the page-level checks. Credential-bearing POSTs now
  require a verified token. The gate lives in the route handler, so the
  server actions (which call auth.api.* in-process) are unaffected. GET
  is untouched for OAuth callbacks and verify-email links, and
  /sign-in/social stays open since it only redirects to the provider.

- Turnstile tokens expire after ~5 minutes and the widget never reset,
  so a form left open submitted a stale token and failed with "complete
  the verification challenge" despite the challenge visibly passing.

Verified with Cloudflare's test keys: all four auth forms block an
invalid token, pass a valid one through to real auth logic, and the API
gate returns 403 without a token and 401 with one.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

components/shared/turnstile-widget.tsx

@@ -38,6 +38,23 @@ export function TurnstileWidget({ className }: { className?: string }) {
       widgetIdRef.current = window.turnstile.render(containerRef.current, {
         sitekey: siteKey,
         theme: "dark",
+        // A Turnstile token is only valid for ~5 minutes. Without these the
+        // widget goes quietly stale on a form left open, and the submit fails
+        // server-side with "complete the verification challenge" even though
+        // the challenge visibly passed. Re-running it keeps the hidden
+        // cf-turnstile-response input fresh.
+        "refresh-expired": "auto",
+        "expired-callback": () => {
+          if (widgetIdRef.current) window.turnstile?.reset(widgetIdRef.current)
+        },
+        "timeout-callback": () => {
+          if (widgetIdRef.current) window.turnstile?.reset(widgetIdRef.current)
+        },
+        "error-callback": () => {
+          // Returning false lets Turnstile surface its own error UI rather than
+          // leaving an empty box the user can't act on.
+          return false
+        },
       })
     }