feat(site): BitGate landing page, integration guide, and live demo

A sibling of the BitLogin design system rather than a twin: the same
ink/paper/brass foundation and serif display, with verdigris — the patina brass
takes as it ages — where BitLogin uses its violet seal.

- index: the signature visual is the product's whole argument, one listing
  reaching four surfaces and getting four different verdicts
- docs: five-step integration, elements table, presets, common mistakes
- demo: the real engine running in the browser against an in-memory transport,
  so nothing is fetched or published. Add reports, restrict the seller, switch
  moderator identities, and watch every surface re-decide.

The widget bundle now re-exports the runtime and core entry points, because a
static page has no package manager — anything it might need has to be reachable
from the one file it loads.

Also fixes the site build reusing a stale widget bundle. It only rebuilt when
the file was missing, which is precisely how a broken demo ships: the page
loads, the module resolves, and an export added since the last build is
silently absent. Caught by running it.

vercel.json mirrors BitLogin's security headers, with connect-src widened to
wss: for relay traffic.

packages/widget/src/index.js

@@ -8,6 +8,30 @@
 // Elements receive a runtime rather than creating one, so a host application
 // can share a single governance runtime across an entire page.
 
+// The bundle is the browser distribution of BitGate as a whole, not only its
+// elements: a static page has no package manager, so anything it might need
+// has to be reachable from this one file.
+export {
+  createBitGate,
+  createCommands,
+  createRelayTransport,
+  createMemoryTransport,
+  createMemoryStorage,
+  ERROR_CODES,
+} from "@bitgate/runtime";
+
+export {
+  SOCIAL_POLICY,
+  COMMERCE_POLICY,
+  ADMIN_ONLY_POLICY,
+  POLICY_PRESETS,
+  getPolicyPreset,
+  createPolicyDefinition,
+  createApplicationAdapter,
+  evaluateObject,
+  collectTargets,
+} from "@bitgate/core";
+
 export {
   BASE_STYLES,
   GovernanceElement,