Extensions UI: own Advertised Extensions section + 'Client Advertised Extensions' heading (#1748)

* Settings: move Advertised Extensions to its own accordion section (#1747)

The Advertised Extensions control (added in #1739) lived inside the Options
accordion panel, wedged between "Fetch Lists One Page at a Time" and "Network
Log Size". Promote it to its own top-level "Advertised Extensions" accordion
section (after Options), so the distinct concept — which extensions the
Inspector advertises to this server in its client capabilities — reads as its
own collapsible section.

- ServerSettingsForm: add "extensions" to ServerSettingsSection; move the
  checkbox group into a new Accordion.Item value="extensions". Its description
  moves up into the panel; no behavior change (still folds into
  settings.advertisedExtensions via onAdvertisedExtensionChange).
- ServerSettingsModal: add "extensions" to allSectionsFor so expand/collapse-all
  covers it.
- Tests: the toggle now lives under the new (collapsed-by-default) section, so
  the form tests render it expanded and the modal tests open it first.

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

* Connection Info: rename "Advertised Extensions" heading to "Client Advertised Extensions"

Disambiguates the client-side column from the adjacent "Server Extensions"
column and from the (separate) Server Settings "Advertised Extensions" section.
Label-only change; the value still renders clientCapabilities.extensions.

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

* docs: refresh Connection Info screenshot for the renamed heading

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

* docs: refresh #1747 proof screenshots (fresh capture)

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

* Settings: add AdvertisedExtensions Storybook story (review)

Address the #1748 review's optional note: the new Advertised Extensions
accordion section had no story expanding it, so it wasn't documented in the
visual catalog (the default story expands only ['options']). Add an
AdvertisedExtensions story with expandedSections: ['extensions'] and a
per-server override, showing the default-on and toggled-off checkbox states.

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/ServerSettingsModal/ServerSettingsModal.test.tsx

@@ -175,8 +175,11 @@ describe("ServerSettingsModal", () => {
         onSettingsChange={onSettingsChange}
       />,
     );
-    // The Options section is expanded by default; Tasks is checked (registry
-    // default), so clicking it toggles the override off.
+    // Advertised Extensions is its own accordion section (#1747), collapsed by
+    // default — open it, then toggle Tasks (checked by the registry default) off.
+    await user.click(
+      screen.getByRole("button", { name: "Advertised Extensions" }),
+    );
     await user.click(
       screen.getByRole("checkbox", {
         name: /Tasks \(io\.modelcontextprotocol\/tasks\)/,
@@ -207,6 +210,10 @@ describe("ServerSettingsModal", () => {
         onSettingsChange={onSettingsChange}
       />,
     );
+    // Open the Advertised Extensions section (#1747), then re-check Tasks.
+    await user.click(
+      screen.getByRole("button", { name: "Advertised Extensions" }),
+    );
     await user.click(
       screen.getByRole("checkbox", {
         name: /Tasks \(io\.modelcontextprotocol\/tasks\)/,

clients/web/src/components/groups/ServerSettingsModal/ServerSettingsModal.tsx

@@ -26,6 +26,7 @@ function allSectionsFor(
 ): ServerSettingsSection[] {
   return [
     "options",
+    "extensions",
     ...(isStdio ? (["environment"] as const) : []),
     "headers",
     "metadata",