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/utils/departments.py

@@ -0,0 +1,21 @@
+"""Shared helpers for resolving the department that owns a given task type."""
+from typing import Optional
+
+
+def find_owning_department(db_project, task_type: str) -> Optional[str]:
+    """Return the name of the department (standard or custom) whose task_types
+    list contains task_type for this project, or None if no department owns it."""
+    if not task_type:
+        return None
+
+    from routers.projects import STANDARD_DEPARTMENTS
+
+    for department in STANDARD_DEPARTMENTS:
+        if task_type in department["task_types"]:
+            return department["name"]
+
+    for department in (db_project.custom_departments or []):
+        if task_type in department.get("task_types", []):
+            return department["name"]
+
+    return None