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.

backend/schemas/department.py

@@ -0,0 +1,50 @@
+"""
+Pydantic schemas for department management
+"""
+from pydantic import BaseModel, Field, validator
+from typing import List
+import re
+
+
+class CustomDepartmentCreate(BaseModel):
+    """Schema for creating a new custom department"""
+    department: str = Field(..., min_length=2, max_length=50, description="Department name")
+
+    @validator('department')
+    def validate_department_name(cls, v):
+        """Validate department name format"""
+        if not re.match(r'^[a-z0-9_]{2,50}$', v):
+            raise ValueError(
+                'Department name must be 2-50 characters, lowercase alphanumeric with underscores only'
+            )
+        return v
+
+
+class CustomDepartmentUpdate(BaseModel):
+    """Schema for updating a custom department name"""
+    old_name: str = Field(..., description="Current department name")
+    new_name: str = Field(..., min_length=2, max_length=50, description="New department name")
+
+    @validator('new_name')
+    def validate_department_name(cls, v):
+        """Validate department name format"""
+        if not re.match(r'^[a-z0-9_]{2,50}$', v):
+            raise ValueError(
+                'Department name must be 2-50 characters, lowercase alphanumeric with underscores only'
+            )
+        return v
+
+
+class AllDepartmentsResponse(BaseModel):
+    """Schema for response containing all departments (standard + custom)"""
+    departments: List[str] = Field(..., description="All departments")
+    standard_departments: List[str] = Field(..., description="Standard departments (read-only)")
+    custom_departments: List[str] = Field(..., description="Custom departments")
+
+
+class DepartmentInUseError(BaseModel):
+    """Schema for error when trying to delete a department in use"""
+    error: str = Field(..., description="Error message")
+    department: str = Field(..., description="Department that is in use")
+    member_count: int = Field(..., description="Number of project members using this department")
+    task_count: int = Field(..., description="Number of tasks using this department")