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.

src/api/routes/category.js

@@ -16,6 +16,7 @@ function categoryErrorStatus(error) {
     if (error.message === 'Name required') return 400;
     if (error.message === 'Category not found') return 404;
     if (error.message === 'Invalid category order') return 400;
+    if (error.message === 'Invalid parent') return 400;
     return 500;
 }
 
@@ -494,4 +495,102 @@ export function register(app, basePath = '') {
             res.status(status).json({ error: error.message });
         }
     });
+
+    /**
+     * @openapi
+     * /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
+     *       the same authorized company. Moving into itself or into a descendant
+     *       (cycle) fails with `Invalid parent`. The moved category gets the next
+     *       sibling `sort` under the new parent.
+     *     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:
+     *               $ref: '#/components/schemas/Error'
+     */
+    app.post(`${basePath}/category/:id/move`, async (req, res) => {
+        const id = Number(req.params.id);
+        if (!Number.isInteger(id) || id <= 0) {
+            return res.status(400).json({ error: 'id is required' });
+        }
+
+        const parentId = Number(req.body?.parentId);
+        if (!Number.isInteger(parentId) || parentId <= 0) {
+            return res.status(400).json({ error: 'parentId is required' });
+        }
+
+        try {
+            const category = await db.move({ googleAuthId: req.user.id, id, parentId });
+            res.status(200).json({ category });
+        } catch (error) {
+            const status = categoryErrorStatus(error);
+            if (status === 500) console.error('Move category failed:', error);
+            res.status(status).json({ error: error.message });
+        }
+    });
 }