error Datable id=example can't reinitialize data table?

Try this

$(document).ready(function () {
    // Create a variable to store the DataTable instance
    var table;

    $('#PrintServer-select').change(function () {
        var printserverId = $(this).val();
        if (printserverId) {
            console.log(printserverId);
            $.ajax({
                url: '',
                type: "GET",
                dataType: "json",
                data: { printserverId: printserverId },
                success: function (data) {
                    console.log(data);
                    $('#branch-select').empty();
                    $.each(data, function (i, item) {
                        $('#branch-select').append($('', {
                            value: item.branchId,
                            text: item.vBranchDesc
                        }));
                    });
                    
                    // Destroy the existing DataTable instance if it exists
                    if (table && $.fn.DataTable.isDataTable('#example')) {
                        table.destroy();
                    }
                    
                    // Hide the table using jQuery
                    $('#example').hide();

                    // Reinitialize the DataTable
                    table = $('#example').DataTable({
                        paging: false
                    });
                }
            });
        }
    });

    // Initialize the DataTable outside of the change event
    table = $("#example").DataTable({
        "bFilter": false,
        "bSort": false,
        "paging": true,
        "bPaginate": true,
        "pagingType": "full_numbers",
        "columnDefs": [
            { className: "pad-md-left-p-10 pad-top-bottom-p-10", "targets": [0, 1, 2, 3, 4, 5, 6, 7] }
        ],
        "lengthMenu": [[5, 10, 15, 20, 25, 35, 50, 100, -1], [5, 10, 15, 20, 25, 35, 50, 100, "All"]],
        "pageLength": 10 // Set the default page length to 10
    });

    // Optional: Destroy the DataTable instance on document unload to prevent memory leaks
    $(window).on('beforeunload', function () {
        if (table && $.fn.DataTable.isDataTable('#example')) {
            table.destroy();
        }
    });
});