Extensions: Connection Info both eras + io.modelcontextprotocol/ui advertisement (Phase 3 of #1633) (#1744)

* Extensions: Connection Info both eras + io.modelcontextprotocol/ui advertisement (Phase 3 of #1633)

Completes the Extensions surfacing and advertises the MCP Apps UI extension.

core/mcp/extensions.ts:
- Add UI_EXTENSION_KEY ("io.modelcontextprotocol/ui") and MCP_APP_MIME_TYPE
  ("text/html;profile=mcp-app") — mirrors of ext-apps' EXTENSION_ID /
  RESOURCE_MIME_TYPE (hardcoded: the constants live on the package's /server
  subpath or an extensionless re-export that doesn't resolve under NodeNext).
- Registry entries gain an optional `advertisement` value; the builder stamps
  it (default {}). Add the `ui` entry, default-advertised with
  `{ mimeTypes: ["text/html;profile=mcp-app"] }` — the Inspector always renders
  App tools. No ext-apps cast needed: the extensions value type is `object`.

ConnectionInfoContent:
- Source server extensions from the negotiated `capabilities.extensions`
  (getServerCapabilities, era-transparent) instead of the modern-only
  discoverResult, so a LEGACY server advertising extensions renders them too.
- Add a two-column "Server Extensions" / "Advertised Extensions" section (the
  Inspector's own advertised map), mirroring the server/client capability
  columns. Drop the now-redundant Extensions row from the modern Discovery
  section (Supported versions stays).

Tests: extensions.test.ts covers the ui entry + advertisement value and the
per-extension enable/disable; ConnectionInfoContent.test.tsx covers legacy
server extensions (no discovery), the advertised-extensions column, and the
em-dash empty states. npm run ci green (the one InspectorView localStorage
failure is a known flake, passes on re-run).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01XNdjEPKLG637X8YmhDiEk5

* Extensions: address Phase 3 review (mime drift-guard, story, exact em-dashes)

- extensions-mimetype.test.ts (integration/node): assert MCP_APP_MIME_TYPE
  equals ext-apps' real RESOURCE_MIME_TYPE (imported) and that the client
  advertises it — a genuine drift guard, replacing the tautological literal
  check in the unit test (which now just asserts the type).
- ConnectionInfoContent Modern story: carry the tasks extension on
  initializeResult.capabilities too, so the Server Extensions row demonstrates
  it (the row now reads negotiated server capabilities, not discoverResult).
- Tighten the em-dash assertions from ">= N" to exact counts (3/3/2) now that
  the two extension sections em-dash by default.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01XNdjEPKLG637X8YmhDiEk5

* Extensions: drift-guard UI_EXTENSION_KEY against ext-apps EXTENSION_ID (review)

Address the Phase 3 re-review nit: the extension id was the other half of the
same drift risk (a server keys its Apps lookup on it). Import ext-apps'
EXTENSION_ID from the /server subpath in the node integration test (fine there;
the browser build is what avoids /server) and assert UI_EXTENSION_KEY === it.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01XNdjEPKLG637X8YmhDiEk5

* Extensions: clone the registry advertisement so builds never alias it (review)

Address the Phase 3 re-review's optional defensive nit: buildClientExtensions
returned the same object reference as the ADVERTISABLE_EXTENSIONS entry for the
ui advertisement, so an in-place mutation of a stamped value (e.g.
extensions[ui].mimeTypes) could corrupt the registry for later connections.
structuredClone the advertisement on stamp; add a test asserting a mutated
build doesn't leak into the next one. Nothing mutates it today — purely
defensive.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01XNdjEPKLG637X8YmhDiEk5

* Extensions: add #1740 Connection Info proof screenshots

End-to-end smoke test in the web client against the legacy
advertised-extensions-http.json server: the Connection Info modal shows the new
era-transparent Server Extensions / Advertised Extensions section, with
Advertised Extensions listing io.modelcontextprotocol/tasks + io.modelcontextprotocol/ui
(the new ui advertisement), and only ui after toggling Tasks off and reconnecting.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01XNdjEPKLG637X8YmhDiEk5

---------

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

core/mcp/extensions.ts

@@ -10,6 +10,25 @@ import { TASKS_EXTENSION_KEY } from "./modernTaskSchemas.js";
 export const EMA_EXTENSION_KEY =
   "io.modelcontextprotocol/enterprise-managed-authorization";
 
+/**
+ * Extension identifier for the MCP Apps UI extension (SEP-ext-apps). Mirrors
+ * `EXTENSION_ID` from `@modelcontextprotocol/ext-apps`. Hardcoded rather than
+ * imported: that constant lives on the package's `/server` subpath, which would
+ * pull server-only code into the browser bundle. The Inspector always renders
+ * MCP Apps, so this is advertised by default (#1740).
+ */
+export const UI_EXTENSION_KEY = "io.modelcontextprotocol/ui";
+
+/**
+ * The MCP Apps UI resource MIME type the Inspector renders. Mirrors
+ * `RESOURCE_MIME_TYPE` from `@modelcontextprotocol/ext-apps`; a server checks
+ * for it in the client's advertised `io.modelcontextprotocol/ui` `mimeTypes` to
+ * decide whether to serve an App. Hardcoded (stable spec string) because
+ * ext-apps re-exports it through an extensionless path that doesn't resolve
+ * cleanly under NodeNext — see the same note in `core/mcp/apps.ts`.
+ */
+export const MCP_APP_MIME_TYPE = "text/html;profile=mcp-app";
+
 /**
  * The value the client stamps for each advertised extension. The wire shape is
  * `{ [extensionId]: object }` (per `ClientCapabilities.extensions`); an empty
@@ -35,6 +54,12 @@ export interface AdvertisableExtension {
    * no explicit preference (the toggle's default position).
    */
   defaultAdvertised: boolean;
+  /**
+   * The object value stamped into `capabilities.extensions[key]` when
+   * advertised. Defaults to `{}` (declared, no sub-options); an extension that
+   * carries settings — e.g. the UI extension's `mimeTypes` — sets its own shape.
+   */
+  advertisement?: ExtensionAdvertisement;
 }
 
 /**
@@ -53,6 +78,15 @@ export const ADVERTISABLE_EXTENSIONS: readonly AdvertisableExtension[] = [
     // (server-directed task creation). Harmless on legacy (extensions ignored).
     defaultAdvertised: true,
   },
+  {
+    key: UI_EXTENSION_KEY,
+    label: "MCP Apps UI (io.modelcontextprotocol/ui)",
+    // The MCP Apps UI extension. The Inspector always renders App tools, so it
+    // advertises this by default with the App resource MIME type it supports —
+    // a conforming server checks the `mimeTypes` before serving a UI resource.
+    defaultAdvertised: true,
+    advertisement: { mimeTypes: [MCP_APP_MIME_TYPE] },
+  },
 ];
 
 export interface BuildClientExtensionsInput {
@@ -83,7 +117,13 @@ export function buildClientExtensions(
   for (const ext of ADVERTISABLE_EXTENSIONS) {
     const advertised = input.advertised?.[ext.key] ?? ext.defaultAdvertised;
     if (advertised) {
-      map[ext.key] = {};
+      // Clone the registry advertisement so the returned map never aliases the
+      // shared `ADVERTISABLE_EXTENSIONS` entry — a later in-place mutation of a
+      // stamped value (e.g. `extensions[ui].mimeTypes`) can't corrupt the
+      // registry for subsequent connections. `{}` entries are fresh literals.
+      map[ext.key] = ext.advertisement
+        ? structuredClone(ext.advertisement)
+        : {};
     }
   }
   if (input.enterpriseManaged) {