Add project Schedule page with interactive Gantt chart

Adds a Schedule tab (Kitsu-style production schedule) under each
project: tasks grouped by type with drag-to-reschedule bars, Day/Week/
Month zoom, manual date-range control, weekend shading, a frozen task
column, and a two-tier month/date axis header. Requires a new
start_date field on Task (start_date was previously missing; only
deadline existed) and shadcn DatePicker inputs replace native date
inputs on the Schedule toolbar and TaskDetailPanel's Start Date/
Deadline fields.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

backend/schemas/task.py

@@ -11,6 +11,7 @@ class TaskBase(BaseModel):
     name: str = Field(..., min_length=1, max_length=255)
     description: Optional[str] = None
     task_type: str  # Changed from TaskType enum to str to support custom task types
+    start_date: Optional[date] = None
     deadline: Optional[date] = None
     status: str = "not_started"  # Changed from TaskStatus enum to str to support custom statuses
 
@@ -27,6 +28,7 @@ class TaskUpdate(BaseModel):
     name: Optional[str] = Field(None, min_length=1, max_length=255)
     description: Optional[str] = None
     task_type: Optional[str] = None  # Changed from TaskType enum to str to support custom task types
+    start_date: Optional[date] = None
     deadline: Optional[date] = None
     status: Optional[str] = None  # Changed from TaskStatus enum to str to support custom statuses
     assigned_user_id: Optional[int] = None
@@ -68,6 +70,7 @@ class TaskListResponse(BaseModel):
     name: str
     task_type: str  # Changed from TaskType enum to str to support custom task types
     status: str  # Changed from TaskStatus enum to str to support custom statuses
+    start_date: Optional[date] = None
     deadline: Optional[date] = None
     project_id: int
     project_name: str