Add POST /category/:id/move to relocate a category.

Wires up the existing category.move store method (validates source and
target in the same company, rejects self/descendant cycles, assigns the
next sibling sort) behind an authenticated HTTP route, plus @openapi
docs and regenerated API docs.

docs/api/openapi.json

@@ -1424,6 +1424,127 @@
         }
       }
     },
+    "/category/{id}/move": {
+      "post": {
+        "tags": [
+          "Category"
+        ],
+        "summary": "Move category to a new parent",
+        "description": "Moves a category to a new parent. Both source and target must be in\nthe same authorized company. Moving into itself or into a descendant\n(cycle) fails with `Invalid parent`. The moved category gets the next\nsibling `sort` under the new parent.\n",
+        "security": [
+          {
+            "cookieAuth": []
+          }
+        ],
+        "x-markdown": "category/move.md",
+        "parameters": [
+          {
+            "in": "path",
+            "name": "id",
+            "required": true,
+            "schema": {
+              "type": "integer"
+            },
+            "description": "Category id to move"
+          }
+        ],
+        "requestBody": {
+          "required": true,
+          "content": {
+            "application/json": {
+              "schema": {
+                "type": "object",
+                "required": [
+                  "parentId"
+                ],
+                "properties": {
+                  "parentId": {
+                    "type": "integer",
+                    "description": "New parent category id"
+                  }
+                },
+                "example": {
+                  "parentId": 3
+                }
+              }
+            }
+          }
+        },
+        "responses": {
+          "200": {
+            "description": "Moved category",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "type": "object",
+                  "properties": {
+                    "category": {
+                      "type": "object",
+                      "required": [
+                        "id",
+                        "parentId",
+                        "sort"
+                      ],
+                      "properties": {
+                        "id": {
+                          "type": "integer"
+                        },
+                        "parentId": {
+                          "type": "integer"
+                        },
+                        "sort": {
+                          "type": "integer"
+                        }
+                      }
+                    }
+                  }
+                }
+              }
+            }
+          },
+          "400": {
+            "description": "Invalid parent",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "$ref": "#/components/schemas/Error"
+                }
+              }
+            }
+          },
+          "401": {
+            "description": "Unauthorized",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "$ref": "#/components/schemas/Error"
+                }
+              }
+            }
+          },
+          "403": {
+            "description": "Not authorized",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "$ref": "#/components/schemas/Error"
+                }
+              }
+            }
+          },
+          "404": {
+            "description": "Category not found",
+            "content": {
+              "application/json": {
+                "schema": {
+                  "$ref": "#/components/schemas/Error"
+                }
+              }
+            }
+          }
+        }
+      }
+    },
     "/brand": {
       "get": {
         "tags": [