Add shot/asset typing and owned task types to departments

Departments now carry a type (shot or asset) and own a list of task
types (e.g. Animation: blocking/primary_pass/second_pass, Composite:
first_pass/second_pass, plus a new Simulation department), additive to
the existing flat Custom Task Type system. When a task's type belongs
to a department, its department is derived and kept in sync server-side
across create/update paths; Task Type is now editable in the Task
Detail panel and Department options are filtered to the task's
shot/asset scope.

backend/schemas/department.py

@@ -2,23 +2,35 @@
 Pydantic schemas for department management
 """
 from pydantic import BaseModel, Field, validator
-from typing import List
+from typing import List, Literal
 import re
 
+DEPARTMENT_NAME_PATTERN = r'^[a-z0-9_]{2,50}$'
+
 
 class CustomDepartmentCreate(BaseModel):
     """Schema for creating a new custom department"""
     department: str = Field(..., min_length=2, max_length=50, description="Department name")
+    department_type: Literal["shot", "asset"] = Field(..., description="Whether this department applies to shots or assets")
+    task_types: List[str] = Field(default_factory=list, description="Task types owned by this department")
 
     @validator('department')
     def validate_department_name(cls, v):
         """Validate department name format"""
-        if not re.match(r'^[a-z0-9_]{2,50}$', v):
+        if not re.match(DEPARTMENT_NAME_PATTERN, v):
             raise ValueError(
                 'Department name must be 2-50 characters, lowercase alphanumeric with underscores only'
             )
         return v
 
+    @validator('task_types', each_item=True)
+    def validate_task_type_name(cls, v):
+        if not re.match(DEPARTMENT_NAME_PATTERN, v):
+            raise ValueError(
+                'Task type name must be 2-50 characters, lowercase alphanumeric with underscores only'
+            )
+        return v
+
 
 class CustomDepartmentUpdate(BaseModel):
     """Schema for updating a custom department name"""
@@ -28,18 +40,52 @@ class CustomDepartmentUpdate(BaseModel):
     @validator('new_name')
     def validate_department_name(cls, v):
         """Validate department name format"""
-        if not re.match(r'^[a-z0-9_]{2,50}$', v):
+        if not re.match(DEPARTMENT_NAME_PATTERN, v):
             raise ValueError(
                 'Department name must be 2-50 characters, lowercase alphanumeric with underscores only'
             )
         return v
 
 
+class DepartmentTaskTypeCreate(BaseModel):
+    """Schema for adding a task type to a custom department"""
+    task_type: str = Field(..., min_length=2, max_length=50, description="Task type name")
+
+    @validator('task_type')
+    def validate_task_type_name(cls, v):
+        if not re.match(DEPARTMENT_NAME_PATTERN, v):
+            raise ValueError(
+                'Task type name must be 2-50 characters, lowercase alphanumeric with underscores only'
+            )
+        return v
+
+
+class DepartmentTaskTypeUpdate(BaseModel):
+    """Schema for renaming a task type within a custom department"""
+    old_name: str = Field(..., description="Current task type name")
+    new_name: str = Field(..., min_length=2, max_length=50, description="New task type name")
+
+    @validator('new_name')
+    def validate_task_type_name(cls, v):
+        if not re.match(DEPARTMENT_NAME_PATTERN, v):
+            raise ValueError(
+                'Task type name must be 2-50 characters, lowercase alphanumeric with underscores only'
+            )
+        return v
+
+
+class DepartmentInfo(BaseModel):
+    """A single department: its name, whether it applies to shots or assets, and its owned task types"""
+    name: str
+    type: Literal["shot", "asset"]
+    task_types: List[str]
+
+
 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")
+    departments: List[DepartmentInfo] = Field(..., description="All departments")
+    standard_departments: List[DepartmentInfo] = Field(..., description="Standard departments (read-only)")
+    custom_departments: List[DepartmentInfo] = Field(..., description="Custom departments")
 
 
 class DepartmentInUseError(BaseModel):
@@ -48,3 +94,11 @@ class DepartmentInUseError(BaseModel):
     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")
+
+
+class DepartmentTaskTypeInUseError(BaseModel):
+    """Schema for error when trying to delete a department task type in use"""
+    error: str = Field(..., description="Error message")
+    department: str = Field(..., description="Department the task type belongs to")
+    task_type: str = Field(..., description="Task type that is in use")
+    task_count: int = Field(..., description="Number of tasks using this task type")