Add category management UI and service layer

Users can now create, edit, and delete custom categories from Settings → Categories. System categories (45 built-in) are shown read-only. Backend adds update_category() and delete_category() service functions; frontend has a new categories API module and a full CRUD section in SettingsPage with filter tabs, colour picker, and delete confirmation.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

frontend/src/api/categories.ts

@@ -0,0 +1,37 @@
+import { api } from "./client";
+
+export interface Category {
+  id: string;
+  name: string;
+  type: "income" | "expense" | "transfer";
+  icon: string | null;
+  color: string | null;
+  is_system: boolean;
+  parent_id: string | null;
+  sort_order: number;
+}
+
+export interface CategoryCreate {
+  name: string;
+  type: "income" | "expense" | "transfer";
+  color?: string | null;
+  icon?: string | null;
+}
+
+export interface CategoryUpdate {
+  name?: string | null;
+  color?: string | null;
+  icon?: string | null;
+}
+
+export const listCategories = (): Promise<Category[]> =>
+  api.get("/categories").then((r: { data: Category[] }) => r.data);
+
+export const createCategory = (data: CategoryCreate): Promise<Category> =>
+  api.post("/categories", data).then((r: { data: Category }) => r.data);
+
+export const updateCategory = (id: string, data: CategoryUpdate): Promise<Category> =>
+  api.put(`/categories/${id}`, data).then((r: { data: Category }) => r.data);
+
+export const deleteCategory = (id: string): Promise<void> =>
+  api.delete(`/categories/${id}`).then(() => undefined);