Add item to a new sheet using Ui menu and trigger onChange() is not working in google apps script

Case:
I have a case using Ui Menu (onOpen()) to add data to a new sheet when the user clicks it. After that, I want to move the data from the new sheet to another spreadsheet and I'm using onChange() trigger to move the data. The trigger will work when new data is inserted on the New Sheet, but it's not working by not reading any changes that happen on the new sheet.

The Code:
I'm using the onChange(e) to move the newly inserted data on the New Sheet into another spreadsheet. I try to check and get only the active sheet and active column but the onChange(e) trigger is not working to detect when new data is added by Ui Menu to the New Sheet.

function onOpen() {
  var ui = SpreadsheetApp.getUi();
  var menu = ui.createMenu("Move")
    .addItem("Move to new sheet", "MovingData")
    .addToUi();
}

function onChange(e) {
  var ActiveSheet = e.source.getActiveSheet().getName();
  var ActiveColumn = e.source.getActiveCell().getColumn();
  console.log(ActiveSheet);
  console.log(ActiveColumn);
  if (ActiveSheet == "New Sheet" && ActiveColumn == 1) {
    //Moving data to another spreadsheet
  }
}  

function MovingData() {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getSheetByName('Source');
  var data = sheet.getDataRange().getValues();

  var sheet_new = ss.getSheetByName("New Sheet");

  var arr = [];
  for (var i = 0; i < data.length; i++) {
      arr.push(data[i]);
      sheet.getRange(i + 1, 5).setValue("Done")
    
  }
  if (arr != "") {
    var newsheet_lr = sheet_new.getLastRow();
    sheet_new.getRange(newsheet_lr + 1, 1, arr.length, arr[0].length).setValues(arr);
  } 
}

The flow of the process:

From but the onChange(e) trigger is not working to detect when new data is added by Ui Menu to the New Sheet., if you want to execute onChange when MovingData() is run, how about the following modification?

Pattern 1:

In this pattern, the script of onChange is called from MovingData.

function MovingData() {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getSheetByName('Source');
  var data = sheet.getDataRange().getValues();

  var sheet_new = ss.getSheetByName("New Sheet");

  var arr = [];
  for (var i = 0; i < data.length; i++) {
      arr.push(data[i]);
      sheet.getRange(i + 1, 5).setValue("Done")
    
  }
  if (arr != "") {
    var newsheet_lr = sheet_new.getLastRow();
    sheet_new.getRange(newsheet_lr + 1, 1, arr.length, arr[0].length).setValues(arr);
  } 

  // Here, copy and paste the script of "//Moving data to another spreadsheet" in "onChange" function.
}

Pattern 2:

In this pattern, the Spreadsheet service is changed to Sheets API in "MovingData" function. When the cell is edited by Sheets API, the OnChange trigger can be fired. So, when you use this, please enable Sheets API ad Advanced Google services.

function MovingData() {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = ss.getSheetByName('Source');
  var data = sheet.getDataRange().getValues();
  var sheet_new = ss.getSheetByName("New Sheet");
  if (data.length > 0) {
	data.forEach(r => r[4] = "Done");
    Sheets.Spreadsheets.Values.append({ values: data }, ss.getId(), "New Sheet", { valueInputOption: "USER_ENTERED" });
  }
}