feat: rename to BitGate and close the drop-in gap

Renames the project and makes it as easy to adopt as BitLogin, which was the
stated bar and which it did not previously meet.

Rename (ADR 0005): @nostr-governance/* -> @bitgate/*, governance-* elements ->
bitgate-*, createGovernanceRuntime -> createBitGate. "Governance" reads as DAO
voting to this audience and named a category rather than a product; BitGate
names the benefit and joins the bit- family that BitVid and BitRoad compose
with. Domain types keep their names — the product is BitGate, the subject
matter is still governance. The migration plan is left as written; this ADR
records the change rather than rewriting history.

Drop-in distribution (ADR 0006): adopting BitGate meant supplying a transport,
authoring a policy, and wiring every element in JavaScript. Now:

- createRelayTransport(urls) — WebSocket transport with reconnection, backoff,
  subscription replay, and cross-relay dedupe
- policy presets (social, commerce, admin-only) addressable by name; the engine
  still carries no thresholds of its own
- <bitgate-provider> — configuration in markup, with descendants finding the
  runtime through a bubbling context event rather than DOM walking, which
  breaks across shadow boundaries
- npm run build:widget — a self-contained dist/bitgate.js

That last one came from running it in a browser rather than from a test. Bare
specifiers resolve in Node and vitest but not in a browser, so the widget
source worked everywhere except a plain static page — the one place it exists
to serve. The bundle is not committed: consumers build from reviewed source.

Also found by running it: the provider's ready event fires during element
upgrade, before a page that defines elements after parsing can attach a
listener, so it now exposes `ready` as a promise too.

Four bugs fixed along the way, three found by new tests and one by the browser:
admin state stayed silent when a roster change altered capabilities but no
denials; the relay transport sent every subscription twice on connect; the
commerce preset computed a meaningless visibility verdict at checkout and could
hide a listing from its own seller; <bitgate-status> threw on an unusable
decision.

759 tests; lint, typecheck, and both builds clean.

packages/widget/src/index.js

@@ -1,4 +1,4 @@
-// @nostr-governance/widget
+// @bitgate/widget
 //
 // Custom elements built strictly on the published API. They render decisions
 // and issue commands; they compute no policy. If an element here ever needs a
@@ -14,9 +14,18 @@ export {
   canRegisterElements,
   defineElement,
   escapeHtml,
+  requestContext,
   shortenKey,
+  targetFromAttributes,
 } from "./base.js";
 
+export {
+  BitGateError,
+  BitGateProvider,
+  CONTEXT_REQUEST,
+  defineProviderElements,
+} from "./provider.js";
+
 export {
   DEFAULT_REASON_TEXT,
   GovernanceReport,
@@ -35,6 +44,7 @@ export {
 } from "./admin.js";
 
 import { defineAdminElements } from "./admin.js";
+import { defineProviderElements } from "./provider.js";
 import { defineViewerElements } from "./viewer.js";
 
 /**
@@ -46,6 +56,6 @@ import { defineViewerElements } from "./viewer.js";
  *
  * @returns {string[]} Element names newly registered by this call
  */
-export function defineGovernanceElements() {
-  return [...defineViewerElements(), ...defineAdminElements()];
+export function defineBitGateElements() {
+  return [...defineProviderElements(), ...defineViewerElements(), ...defineAdminElements()];
 }