NestedFolderPicker: Migrate to app platform API (#106926)

* Add /children endpoint

* Update folder client

* Add comment

* Add feature toggle

* Add new version of useFoldersQuery

* Error handling

* Format

* Rename feature toggle

* Remove options and move root folder constant

* Fix feature toggle merge

* Add feature toggle again

* Rename useFoldersQuery files

* Update API spec

* Fix test

* Add test

* Better typings

---------

Co-authored-by: Clarity-89 <homes89@ukr.net>

pkg/tests/apis/openapi_snapshots/folder.grafana.app-v1beta1.json

@@ -915,6 +915,55 @@
         }
       ]
     },
+    "/apis/folder.grafana.app/v1beta1/namespaces/{namespace}/folders/{name}/children": {
+      "get": {
+        "tags": [
+          "Folder"
+        ],
+        "description": "connect GET requests to children of Folder",
+        "operationId": "getFolderChildren",
+        "responses": {
+          "200": {
+            "description": "OK",
+            "content": {
+              "*/*": {
+                "schema": {
+                  "$ref": "#/components/schemas/com.github.grafana.grafana.apps.folder.pkg.apis.folder.v1beta1.FolderList"
+                }
+              }
+            }
+          }
+        },
+        "x-kubernetes-action": "connect",
+        "x-kubernetes-group-version-kind": {
+          "group": "folder.grafana.app",
+          "version": "v1beta1",
+          "kind": "FolderList"
+        }
+      },
+      "parameters": [
+        {
+          "name": "name",
+          "in": "path",
+          "description": "name of the FolderList",
+          "required": true,
+          "schema": {
+            "type": "string",
+            "uniqueItems": true
+          }
+        },
+        {
+          "name": "namespace",
+          "in": "path",
+          "description": "object name and auth scope, such as for teams and projects",
+          "required": true,
+          "schema": {
+            "type": "string",
+            "uniqueItems": true
+          }
+        }
+      ]
+    },
     "/apis/folder.grafana.app/v1beta1/namespaces/{namespace}/folders/{name}/counts": {
       "get": {
         "tags": [