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The following code only takes what is visible in the filtered table and copies it to another sheet. Hope this helps!
function main(workbook: ExcelScript.Workbook) {
let firstSheet = workbook.getWorksheet("Sheet1");
let table = firstSheet.getTables()[0]
let visibleTableRange = table.getRange().getVisibleView();
let visibleTableRangeValues = visibleTableRange.getValues();
let sheetToPaste = workbook.getWorksheet("Paste")
let pastedValues = sheetToPaste.getRangeByIndexes(0, 0,
visibleTableRange.getRowCount(), visibleTableRange.getColumnCount());
pastedValues.setValues(visibleTableRangeValues);
let newTable = sheetToPaste.addTable(pastedValues.getAddress(), true)
}