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/models/task.py

@@ -56,6 +56,7 @@ class Task(Base):
     name = Column(String, nullable=False, index=True)
     description = Column(Text)
     status = Column(String, nullable=False, default="not_started")  # Changed from Enum to String to support custom statuses
+    start_date = Column(Date)
     deadline = Column(Date)
     created_at = Column(DateTime(timezone=True), server_default=func.now())
     updated_at = Column(DateTime(timezone=True), server_default=func.now(), onupdate=func.now())