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/components/groups/ConnectionInfoContent/ConnectionInfoContent.test.tsx

@@ -57,7 +57,9 @@ describe("ConnectionInfoContent", () => {
         transport="stdio"
       />,
     );
-    expect(screen.getByText("—")).toBeInTheDocument();
+    // Exactly three em dashes: the missing server version, plus the two
+    // extension sections (the fixtures advertise none on either side).
+    expect(screen.getAllByText("—")).toHaveLength(3);
   });
 
   it("renders server and client capability sections", () => {
@@ -151,12 +153,9 @@ describe("ConnectionInfoContent", () => {
     expect(screen.getByText("Sessionless")).toBeInTheDocument();
     expect(screen.getByText("Discovery")).toBeInTheDocument();
     expect(screen.getByText("2026-07-28, 2025-11-25")).toBeInTheDocument();
-    expect(
-      screen.getByText("io.modelcontextprotocol/tasks"),
-    ).toBeInTheDocument();
   });
 
-  it("renders em-dashes for empty supported versions and absent extensions", () => {
+  it("renders an em-dash for empty supported versions in Discovery", () => {
     renderWithMantine(
       <ConnectionInfoContent
         initializeResult={fullResult}
@@ -171,9 +170,74 @@ describe("ConnectionInfoContent", () => {
       />,
     );
     expect(screen.getByText("Supported versions")).toBeInTheDocument();
-    expect(screen.getByText("Extensions")).toBeInTheDocument();
-    // Both the empty-versions and no-extensions values render as an em dash.
-    expect(screen.getAllByText("—").length).toBeGreaterThanOrEqual(2);
+    // Extensions moved out of Discovery into their own era-transparent section.
+    expect(screen.queryByText("Discovery")).toBeInTheDocument();
+    // Exactly three em dashes: empty supported versions, plus the two extension
+    // sections (the fixtures advertise none).
+    expect(screen.getAllByText("—")).toHaveLength(3);
+  });
+
+  it("shows server extensions on a LEGACY connection (no discovery), from server capabilities (#1740)", () => {
+    renderWithMantine(
+      <ConnectionInfoContent
+        initializeResult={{
+          ...fullResult,
+          capabilities: {
+            ...fullResult.capabilities,
+            extensions: { "io.modelcontextprotocol/tasks": {} },
+          },
+        }}
+        clientCapabilities={fullClientCaps}
+        transport="streamable-http"
+        protocolEra="legacy"
+      />,
+    );
+    // No discoverResult (legacy) but the server's extension still renders,
+    // sourced from the negotiated server capabilities rather than discovery.
+    expect(screen.queryByText("Discovery")).not.toBeInTheDocument();
+    expect(screen.getByText("Server Extensions")).toBeInTheDocument();
+    expect(
+      screen.getByText("io.modelcontextprotocol/tasks"),
+    ).toBeInTheDocument();
+  });
+
+  it("shows the Inspector's own advertised extensions (#1740)", () => {
+    renderWithMantine(
+      <ConnectionInfoContent
+        initializeResult={fullResult}
+        clientCapabilities={{
+          ...fullClientCaps,
+          extensions: {
+            "io.modelcontextprotocol/tasks": {},
+            "io.modelcontextprotocol/ui": { mimeTypes: ["text/html"] },
+          },
+        }}
+        transport="streamable-http"
+        protocolEra="legacy"
+      />,
+    );
+    expect(screen.getByText("Advertised Extensions")).toBeInTheDocument();
+    expect(
+      screen.getByText(
+        "io.modelcontextprotocol/tasks, io.modelcontextprotocol/ui",
+      ),
+    ).toBeInTheDocument();
+  });
+
+  it("renders em-dashes for the extensions sections when neither side advertises any (#1740)", () => {
+    renderWithMantine(
+      <ConnectionInfoContent
+        initializeResult={fullResult}
+        clientCapabilities={fullClientCaps}
+        transport="streamable-http"
+        protocolEra="legacy"
+      />,
+    );
+    expect(screen.getByText("Server Extensions")).toBeInTheDocument();
+    expect(screen.getByText("Advertised Extensions")).toBeInTheDocument();
+    // Exactly two em dashes: the two extension sections (the server version is
+    // present in the fixture, so it does not em-dash).
+    expect(screen.getAllByText("—")).toHaveLength(2);
   });
 
   it("renders client registration kind when provided", () => {