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>

pr-screenshots/README.md

@@ -1,3 +1,37 @@
+# Connection Info extensions + `io.modelcontextprotocol/ui` (#1740) — proof screenshots
+
+End-to-end verification of the Phase 3 Connection Info UI against the legacy
+`advertised-extensions-http.json` test server (port 3220), driven in a real
+browser through the web client's remote-proxy transport.
+
+![Connection Info on a legacy connection — Advertised Extensions shows tasks + ui](advertised-ext-conninfo-legacy.png)
+
+The Connection Info modal on a **legacy** connection (Era: **LEGACY**, no
+Discovery section). The new **Server Extensions / Advertised Extensions**
+two-column section renders — proving it is era-transparent (before #1740,
+extensions only appeared in the modern-only Discovery section). **Advertised
+Extensions** shows `io.modelcontextprotocol/tasks, io.modelcontextprotocol/ui`,
+confirming the Inspector now advertises the MCP Apps `ui` extension. (Server
+Extensions is `—` because this test server advertises none server-side.)
+
+![Connection Info after toggling Tasks off — Advertised Extensions shows only ui](advertised-ext-conninfo-tasksoff.png)
+
+After unchecking **Tasks** in Server Settings → Advertised Extensions (Phase 2)
+and reconnecting, the **Advertised Extensions** column shows only
+`io.modelcontextprotocol/ui` — the display reflects the per-server override live,
+and the `ui` advertisement persists (it is a separate registry entry).
+
+> Note: the Connection Info modal is populated from the connection's
+> `initializeResult`, which requires `serverInfo`. On the modern test server used
+> here `serverInfo` wasn't populated, so the modal stays closed on that modern
+> connection — a pre-existing connection-layer behavior, independent of this PR
+> (which only changes content *inside* the modal). The era-transparent
+> **Server Extensions** path is covered by unit tests
+> (`ConnectionInfoContent.test.tsx` renders legacy server extensions with no
+> `discoverResult`).
+
+---
+
 # Advertised-extensions toggle (#1739) — proof screenshots
 
 End-to-end verification of the advertised-extensions debugging knob against a