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>

clients/web/src/test/integration/mcp/extensions-mimetype.test.ts

@@ -0,0 +1,39 @@
+import { describe, it, expect } from "vitest";
+import { RESOURCE_MIME_TYPE } from "@modelcontextprotocol/ext-apps/app-bridge";
+// EXTENSION_ID lives on ext-apps' `/server` subpath, which the browser build
+// avoids importing — but this node integration test can, so it's the one place
+// the hardcoded key can be checked against the real constant.
+import { EXTENSION_ID } from "@modelcontextprotocol/ext-apps/server";
+import {
+  MCP_APP_MIME_TYPE,
+  UI_EXTENSION_KEY,
+  buildClientExtensions,
+} from "@inspector/core/mcp/extensions.js";
+
+/**
+ * Drift guard for the MCP Apps UI advertisement (#1740). `MCP_APP_MIME_TYPE` is
+ * hardcoded in core (ext-apps' constant lives on a `/server` subpath / an
+ * extensionless re-export that doesn't resolve cleanly under NodeNext in the
+ * browser build). A conforming server checks the client's advertised `mimeTypes`
+ * before serving an App, so if the hardcoded string ever drifts from ext-apps'
+ * real `RESOURCE_MIME_TYPE`, Apps silently stop working against strict servers.
+ *
+ * This runs in the node integration project, where importing the real ext-apps
+ * value resolves — the one place the two can actually be compared.
+ */
+describe("MCP Apps UI extension constants (#1740)", () => {
+  it("MCP_APP_MIME_TYPE matches ext-apps' RESOURCE_MIME_TYPE exactly", () => {
+    expect(MCP_APP_MIME_TYPE).toBe(RESOURCE_MIME_TYPE);
+  });
+
+  it("UI_EXTENSION_KEY matches ext-apps' EXTENSION_ID exactly", () => {
+    // A server keys its Apps lookup on the extension id, so a drifted key
+    // silently disables Apps just like a drifted MIME type.
+    expect(UI_EXTENSION_KEY).toBe(EXTENSION_ID);
+  });
+
+  it("is the value the client actually advertises for the ui extension", () => {
+    const map = buildClientExtensions({ enterpriseManaged: false });
+    expect(map[UI_EXTENSION_KEY]).toEqual({ mimeTypes: [RESOURCE_MIME_TYPE] });
+  });
+});