Use Math.min(), like this:

function test() {
  const ss = SpreadsheetApp.getActive();
  const range = ss.getRange('Sheet1!E2:Z');
  hideSameColumns_(range.getSheet(), ss.getSheetByName('Sheet2'), range.getColumn());
}

function hideSameColumns_(sourceSheet, targetSheet, startColumn = 1) {
  const numColumns = Math.min(sourceSheet.getMaxColumns(), targetSheet.getMaxColumns()) - startColumn + 1;
  for (let i = 0; i < numColumns; i++) {
    const colNumber = startColumn + i;
    if (sourceSheet.isColumnHiddenByUser(colNumber)) targetSheet.hideColumns(colNumber);
  }
}

See Math.min().

Based on your code, you should only replace tempSheet.hideColumns(i+1); with:

tempSheet.hideColumns(originalColumn);

Here’s the code with a sample setup:

function test() {
  //sample setup
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var tempSheet = ss.getSheetByName('Sheet2');
  var sheet = ss.getSheetByName('Sheet1');
  var range = sheet.getRange(1,5,sheet.getLastRow(), sheet.getLastColumn()-4);
  var tempSheet = ss.getSheetByName('Sheet2');
  var sheet = ss.getSheetByName('Sheet1');
  const startColumn = range.getColumn();  // The starting column of the range (e.g., "E" -> 5)
  const numColumns = range.getNumColumns();  // The number of columns in the range

  for (let i = 0; i < numColumns; i++) {
    const originalColumn = startColumn + i;  // Get the original column number
    const columnHidden = sheet.isColumnHiddenByUser(originalColumn);  // Check if the column is hidden in the original sheet
    const ende = tempSheet.getLastColumn();

    // If the column is hidden in the original sheet, hide the corresponding column in the temporary sheet
    if (columnHidden) {
      tempSheet.hideColumns(originalColumn);  // use original column here
    }
    // Logger.log(`start column: ${startColumn + i}, left: ${numColumns - i} , Ende: ${ende} , Checking column: ${originalColumn}, isHidden: ${columnHidden}`);
  }
}

Here’s an alternative code using forEach and ternary operator:

function myFunction() {
  //sample setup
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var tempSheet = ss.getSheetByName('Sheet2');
  var sheet = ss.getSheetByName('Sheet1');
  var range = sheet.getDataRange();
  var tempSheet = ss.getSheetByName('Sheet2');
  var sheet = ss.getSheetByName('Sheet1');
  var startColumn = 5;
  //actual edits
  var data = range.getValues(); //get the 2d array data to get the dimensions for iteration
  data[0].forEach((x, i) => ((i>=startColumn)*(sheet.isColumnHiddenByUser(i + 1)) ? tempSheet.hideColumns(i + 1) : null));

}

The code above does entirely the same thing, and the code that uses forEach and ternary shortens the syntax of your code.

Reference

• forEach