@inject AssignmentDragContainer dragContainer

@code {
  [Parameter]
  [Required]
  public LocalAssignment assignment { get; set; } = new();
  private  async Task HandleDragStart()
  {
    dragContainer.AssignmentBeingDragged = assignment;
  }
}

<div 
  draggable="true"
  ondragstart="HandleDragStart"
  class="col-2"
>
  <div class="card">
    <div class="card-body">
      <div class="card-title">@assignment.name</div>
    </div>
  </div>
</div>