feat: platform AI names behind Sign in with OTM (v0.3.0)

- OTM SSO: /api/auth/otm-sso verifies the control-plane ticket (vendored
  verifier), in-memory jti claim, mints an HMAC cookie (src/lib/session.ts);
  /api/auth/session + /api/auth/signout. No accounts, no DB.
- /api/ai-names: server-side call to the platform's metered gateway
  (ANTHROPIC_BASE_URL + per-app gateway token), 401 without a session,
  ~20 req/h per OTM account. Prompt/parser shared with the BYO-key path
  via src/lib/ai-prompt.ts.
- Finder: 'Sign in with OTM for AI names' link → 'AI names' toggle when
  signed in; own key still overrides.

Pairs with platform 0.116.0 (needsAnthropic + needsAuthSecret on names).

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01XStQKxPfEjrTvWo83KFCxG

src/app/settings/page.tsx

@@ -46,7 +46,8 @@ export default function SettingsPage() {
       <p className="tagline">
         The name finder works fully offline without this &mdash; the built-in generator needs no
         key and costs nothing. Adding your own API key gets you a second, usually more
-        imaginative set of suggestions alongside it.
+        imaginative set of suggestions alongside it. Don&rsquo;t have a key? Sign in with a free
+        OTM account on the main page and AI names are included &mdash; a key here overrides that.
       </p>
 
       <p className="notice info">