fix(shell-docs): fix empty FeatureIntegrations and matrix 404

- Correct 3 mismatched feature IDs in MDX (generative-ui-tool-based ->
  gen-ui-tool-based, frontend-tools-sync -> frontend-tools, reasoning ->
  agentic-chat-reasoning) so FeatureIntegrations renders integration chips
- Remove stale 'matrix' from RESERVED_ROUTE_SLUGS (no app/matrix/ route exists)
- Replace broken /matrix links in IntegrationGrid and search-modal with /
  since the matrix lives in shell-dashboard, not shell-docs

Author: samjulien

showcase/shell-docs/src/app/layout.tsx

@@ -14,7 +14,6 @@ export const RESERVED_ROUTE_SLUGS = [
   "ag-ui",
   "reference",
   "api",
-  "matrix",
 ] as const;
 
 const plusJakartaSans = Plus_Jakarta_Sans({

showcase/shell-docs/src/components/search-modal.tsx

@@ -143,7 +143,7 @@ export function SearchModal({ onClose }: { onClose: () => void }) {
             type: "feature",
             title: f.name,
             subtitle: f.description,
-            href: "/matrix",
+            href: "/",
           });
         }
       }

showcase/shell-docs/src/content/docs/frontend-tools.mdx

@@ -47,7 +47,7 @@ what happened.
 
 <Snippet region="frontend-tool-handler" title="frontend/src/app/page.tsx — handler body" />
 
-<FeatureIntegrations feature="frontend-tools-sync" />
+<FeatureIntegrations feature="frontend-tools" />
 
 ## Get started by choosing your AI backend
 

showcase/shell-docs/src/content/docs/generative-ui/reasoning.mdx

@@ -74,7 +74,7 @@ component to match your product's tone.
   default card. See the reference docs for sub-slot props.
 </Callout>
 
-<FeatureIntegrations feature="reasoning" />
+<FeatureIntegrations feature="agentic-chat-reasoning" />
 
 ## Choose your AI backend
 

showcase/shell-docs/src/content/docs/generative-ui/tool-based.mdx

@@ -56,7 +56,7 @@ donut for the pie chart; neither knows anything about CopilotKit.
   reliably picks it when the user asks for that visualization.
 </Callout>
 
-<FeatureIntegrations feature="generative-ui-tool-based" />
+<FeatureIntegrations feature="gen-ui-tool-based" />
 
 ## Choose your AI backend
 

showcase/shell-docs/src/lib/mdx-registry.tsx

@@ -523,10 +523,10 @@ export const docsComponents = {
       }}
     >
       See the{" "}
-      <a href="/matrix" style={{ color: "var(--accent)" }}>
-        Feature Matrix
+      <a href="/" style={{ color: "var(--accent)" }}>
+        integrations overview
       </a>{" "}
-      for a full comparison.
+      for all available frameworks.
     </div>
   ),
   IntegrationsGrid: ({ children }: { children?: React.ReactNode }) => (