Extend PATCH /category/:id to also move (parentId) alongside rename.

PATCH now accepts name (rename, re-slugify) and/or parentId (move under a
new parent, cycle/self guarded), merging both results. Renames the PATCH
docs file to category/update.md and regenerates API docs.

docs/api/routes/category/update.md

@@ -0,0 +1,48 @@
+# `PATCH /category/{id}`
+
+Protected. Requires a valid session cookie (`credentials: 'include'`).
+
+Update category (rename or move)
+
+Updates a category the user is authorized for.
+`name` renames the category (re-slugifies in the company default language).
+`parentId` moves it under a new parent (cycle/self → `Invalid parent`).
+Either `name` or `parentId` (or both) is required.
+
+
+## Path parameters
+
+| Param | Required | Type | Description |
+|-------|----------|------|-------------|
+| `id` | yes | integer | Category id |
+
+## Body (JSON)
+
+```json
+{
+  "parentId": 3
+}
+```
+
+## Response `200`
+
+Updated category (renamed and/or moved)
+
+```json
+{
+  "category": { … }
+}
+```
+
+## Errors
+
+| Status | Description |
+|--------|-------------|
+| 400 | Validation error (name or parentId required, or invalid parent) — `{"error":"…"}` |
+| 401 | Unauthorized — `{"error":"…"}` |
+| 403 | Not authorized — `{"error":"…"}` |
+| 404 | Category not found — `{"error":"…"}` |
+
+---
+
+_Generated from `@openapi` JSDoc. Do not edit by hand — run `npm run docs:api`._