Extensions: advertised-extensions toggle in Server Settings (Phase 2 of #1633) (#1743)

* Extensions: advertised-extensions toggle in Server Settings (Phase 2 of #1633)

Adds the debugging knob from #1633: users choose which extensions the
Inspector advertises to a server, and a server may register different tools
in response. Builds on Phase 1's registry + advertisedExtensions option (#1738).

Settings + persistence (core):
- InspectorServerSettings.advertisedExtensions + StoredMCPServer field, wired
  through serverList's read/write converters and INSPECTOR_FIELD_KEY_MAP
  (omit-when-empty, byte-stable round-trip).
- validateSettings (remote PUT route): isBooleanRecord guard + carry a
  non-empty map; unknown/malformed rejected.
- App.tsx threads savedSettings.advertisedExtensions into the client options.

UI:
- ServerSettingsForm renders an "Advertised Extensions" group of checkboxes
  driven by ADVERTISABLE_EXTENSIONS; a per-server override wins over the
  registry default. Modal folds a toggle into settings.advertisedExtensions.

Test server + proof:
- composable-test-server extensionGatedTools: a tool registered disabled and
  enabled on `initialized` iff the client declared the mapped extension
  (getClientCapabilities). Legacy stateful leg. Threaded through
  load-config/resolve-config; advertised-extensions-http.json showcase + README.
- Integration test connects legacy with/without the tasks extension advertised
  and asserts the gated tool appears/disappears in tools/list — the acceptance
  criterion, proven end to end, not asserted.

Tests: serverList round-trip (non-empty/absent/empty), ServerSettingsForm
toggle rows, ServerSettingsModal fold, validateSettings accept/reject, and the
integration gating test. npm run ci green (per-file ≥90 gate held).

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

* Extensions: add #1739 proof screenshots (advertised-extensions toggle)

End-to-end smoke test in the web client against the legacy
advertised-extensions-http.json test server (port 3220): connecting with the
Tasks extension advertised (default) lists echo + get_weather, unchecking the
Advertised Extensions → Tasks toggle and reconnecting lists only echo — the
server's tool registration changing on the client-declared extension.

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

* Extensions: reconverge advertisedExtensions to no-override on default (review)

Address Phase 2 review observation #1: toggling an extension back to its
registry default now deletes the override key (and drops the whole map to
undefined when it empties), so the on-disk `advertisedExtensions` reconverges
to the byte-stable "no override" state instead of persisting a redundant
`{ key: <default> }`. Matches the omit-when-default policy the other settings
use. Only a value that differs from the default is persisted.

Adds a modal test asserting the reconvergence (re-checking the sole disabling
override drops advertisedExtensions to undefined).

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/core/mcp/serverList.test.ts

@@ -284,6 +284,63 @@ describe("serverEntriesToMcpConfig", () => {
     expect(round).toEqual(original);
   });
 
+  it("round-trips advertisedExtensions: lifts a non-empty map to settings and back to disk", () => {
+    const original: MCPConfig = {
+      mcpServers: {
+        exttest: {
+          type: "streamable-http",
+          url: "https://x.test/mcp",
+          advertisedExtensions: { "io.modelcontextprotocol/tasks": false },
+        },
+      },
+    };
+    const [entry] = mcpConfigToServerEntries(original);
+    expect(entry?.settings?.advertisedExtensions).toEqual({
+      "io.modelcontextprotocol/tasks": false,
+    });
+    const round = serverEntriesToMcpConfig(mcpConfigToServerEntries(original));
+    expect(round).toEqual(original);
+  });
+
+  it("omits advertisedExtensions from disk when unset, and leaves settings unset", () => {
+    const original: MCPConfig = {
+      mcpServers: {
+        extnone: {
+          type: "streamable-http",
+          url: "https://x.test/mcp",
+          connectionTimeout: 5000,
+        },
+      },
+    };
+    const [entry] = mcpConfigToServerEntries(original);
+    expect(entry?.settings?.advertisedExtensions).toBeUndefined();
+    const round = serverEntriesToMcpConfig(mcpConfigToServerEntries(original));
+    expect("advertisedExtensions" in (round.mcpServers.extnone ?? {})).toBe(
+      false,
+    );
+    expect(round).toEqual(original);
+  });
+
+  it("treats an empty advertisedExtensions map on disk as unset (omitted on write)", () => {
+    const original: MCPConfig = {
+      mcpServers: {
+        extempty: {
+          type: "streamable-http",
+          url: "https://x.test/mcp",
+          advertisedExtensions: {},
+        },
+      },
+    };
+    const [entry] = mcpConfigToServerEntries(original);
+    // An empty map reads back as unset for the form...
+    expect(entry?.settings?.advertisedExtensions).toBeUndefined();
+    // ...and the write side omits it, so the empty map does not round-trip.
+    const round = serverEntriesToMcpConfig(mcpConfigToServerEntries(original));
+    expect("advertisedExtensions" in (round.mcpServers.extempty ?? {})).toBe(
+      false,
+    );
+  });
+
   it("round-trips maxFetchRequests: lifts a non-default value to settings and back to disk", () => {
     const original: MCPConfig = {
       mcpServers: {