I have that same problem and i decide make solution adding scroll to calendar

    ::ng-deep .p-datepicker {
    position: absolute;
    top: 100%;
    left: 0;
    z-index: 9999;
    font-size: 0.8rem;
    height : 200px;
    
    // does scrollable
    max-height: 300px; // adjust this value maybe your needs
    overflow-y: auto;
    
    // Opcional: for a scrollbar
    &::-webkit-scrollbar {
      width: 8px;
    }
    
    &::-webkit-scrollbar-track {
      background: #f1f1f1;
      border-radius: 4px;
    }
    
    &::-webkit-scrollbar-thumb {
      background: #888;
      border-radius: 4px;
      
      &:hover {
        background: #555;
      }
    }
  }

Have a good day! and i've hope to help you.