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/integration/mcp/remote/server-extra-coverage.test.ts

@@ -513,6 +513,27 @@ describe("server.ts supplemental coverage", () => {
       expect((await res.json()).error).toMatch(/modernLogLevel/);
     });
 
+    it("rejects a non-boolean-valued advertisedExtensions (#1739)", async () => {
+      const res = await postSettings({
+        ...base,
+        advertisedExtensions: { "io.modelcontextprotocol/tasks": "yes" },
+      });
+      expect((await res.json()).error).toMatch(/advertisedExtensions/);
+    });
+
+    it("rejects a non-object advertisedExtensions (#1739)", async () => {
+      const res = await postSettings({
+        ...base,
+        advertisedExtensions: ["io.modelcontextprotocol/tasks"],
+      });
+      expect((await res.json()).error).toMatch(/advertisedExtensions/);
+    });
+
+    it("accepts an empty advertisedExtensions map without persisting it (#1739)", async () => {
+      const res = await postSettings({ ...base, advertisedExtensions: {} });
+      expect(res.status).toBe(200);
+    });
+
     it("accepts a fully-populated valid settings payload", async () => {
       const res = await postSettings({
         ...base,
@@ -521,6 +542,7 @@ describe("server.ts supplemental coverage", () => {
         taskTtl: 1000,
         autoRefreshOnListChanged: true,
         paginatedLists: true,
+        advertisedExtensions: { "io.modelcontextprotocol/tasks": false },
         maxFetchRequests: 5,
         protocolEra: "modern",
         modernLogLevel: "off",