docs: add interactive API reference using docusaurus-openapi-docs (#37434)

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

docs/sidebars.js

@@ -107,9 +107,21 @@ const sidebars = {
       id: 'faq',
     },
     {
-      type: 'doc',
-      label: 'API',
-      id: 'api',
+      type: 'category',
+      label: 'API Reference',
+      link: {
+        type: 'doc',
+        id: 'api',
+      },
+      items: (() => {
+        try {
+          // eslint-disable-next-line @typescript-eslint/no-require-imports
+          return require('./docs/api/sidebar.js');
+        } catch {
+          // Generated by `yarn generate:api-docs`; empty until then
+          return [];
+        }
+      })(),
     },
   ],
 };