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.

docs/integration-guide.md

@@ -25,7 +25,7 @@ revision was bad. Most objects want both.
 ## 2. Write an adapter
 
 ```js
-import { createApplicationAdapter } from "@nostr-governance/core";
+import { createApplicationAdapter } from "@bitgate/core";
 
 export const productAdapter = createApplicationAdapter({
   applicationId: "my-shop",
@@ -64,7 +64,7 @@ A policy is a set of named **profiles**, one per surface. Profiles read the same
 evidence and are free to reach different conclusions.
 
 ```js
-import { createPolicyDefinition } from "@nostr-governance/core";
+import { createPolicyDefinition } from "@bitgate/core";
 
 export const policy = createPolicyDefinition({
   id: "my-shop",
@@ -145,13 +145,13 @@ A signer (`getPublicKey`, `signEvent`) and storage (`read`, `write`, `remove`)
 follow the same injection pattern. In-memory versions ship for testing:
 
 ```js
-import { createMemoryTransport, createMemoryStorage } from "@nostr-governance/runtime";
+import { createMemoryTransport, createMemoryStorage } from "@bitgate/runtime";
 ```
 
 ## 5. Wire the pipeline
 
 ```js
-import { collectTargets, evaluateObject } from "@nostr-governance/core";
+import { collectTargets, evaluateObject } from "@bitgate/core";
 
 runtime.setViewer(viewerPubkey);        // do this FIRST — it clears viewer state
 runtime.trust.setContacts(followList);  // then seed trust
@@ -178,7 +178,7 @@ seed contacts, blocks, and overrides *after* it, never before.
 Roles are application-defined bundles over a fixed capability vocabulary:
 
 ```js
-import { createRoleDefinition } from "@nostr-governance/core";
+import { createRoleDefinition } from "@bitgate/core";
 
 const roles = {
   listing_moderator: createRoleDefinition("listing_moderator", [
@@ -227,7 +227,7 @@ systems are deliberately separate.
 The conformance harness takes JSON fixtures and asserts decisions:
 
 ```js
-import { runConformanceCase } from "@nostr-governance/testing/conformance";
+import { runConformanceCase } from "@bitgate/testing/conformance";
 
 const { passed, mismatches } = runConformanceCase(fixture, policy);
 ```