Add per-project Department management

Departments are now a customizable per-project list (standard + custom),
matching the existing custom task type/status pattern, instead of a fixed
7-value enum. They're usable directly on tasks (new field, independent of
assignee) and continue to drive team member department roles.

frontend/src/services/department.ts

@@ -0,0 +1,47 @@
+import { apiClient } from './api'
+
+export interface AllDepartmentsResponse {
+  departments: string[]
+  standard_departments: string[]
+  custom_departments: string[]
+}
+
+export interface CustomDepartmentCreate {
+  department: string
+}
+
+export interface CustomDepartmentUpdate {
+  old_name: string
+  new_name: string
+}
+
+export interface DepartmentInUseError {
+  error: string
+  department: string
+  member_count: number
+  task_count: number
+}
+
+export const departmentService = {
+  async getAllDepartments(projectId: number): Promise<AllDepartmentsResponse> {
+    const response = await apiClient.get(`/projects/${projectId}/departments`)
+    return response.data
+  },
+
+  async addDepartment(projectId: number, data: CustomDepartmentCreate): Promise<AllDepartmentsResponse> {
+    const response = await apiClient.post(`/projects/${projectId}/departments`, data)
+    return response.data
+  },
+
+  async updateDepartment(projectId: number, department: string, data: CustomDepartmentUpdate): Promise<AllDepartmentsResponse> {
+    const encodedDepartment = encodeURIComponent(department)
+    const response = await apiClient.put(`/projects/${projectId}/departments/${encodedDepartment}`, data)
+    return response.data
+  },
+
+  async deleteDepartment(projectId: number, department: string): Promise<AllDepartmentsResponse> {
+    const encodedDepartment = encodeURIComponent(department)
+    const response = await apiClient.delete(`/projects/${projectId}/departments/${encodedDepartment}`)
+    return response.data
+  }
+}