I have to use the following:
def add_row_and_adjust_banding(service, spreadsheet_id, sheet_name, new_row):
  """
  Adds a row to a sheet and adjusts the existing banded range accordingly.

  Args:
    service: The Google Sheets API service object.
    spreadsheet_id: The ID of the spreadsheet.
    sheet_name: The name of the sheet.
    new_row: A list representing the values for the new row.

  Returns:
    The result of the batchUpdate operation.
  """

  # Get the sheet ID
  sheet_metadata = service.spreadsheets().get(spreadsheetId=spreadsheet_id,
                                             fields='sheets.properties.sheetId,sheets.properties.title').execute()
  our_sheet = None
  for sheet in sheet_metadata.get('sheets', []):
    if sheet['properties']['title'] == sheet_name:
      our_sheet = sheet
      break
  else:
    raise ValueError(f"Sheet '{sheet_name}' not found.")

  # Add the new row
  append_request_body = {
      'requests': [{
          'appendCells': {
              'rows': [
                  {'values': [{'userEnteredValue': {'stringValue': str(val)}} for val in new_row]}
              ],
              'sheetId': our_sheet['properties']['sheetId'],
              'fields': 'userEnteredValue'
          }
      }]
  }
  append_result = service.spreadsheets().batchUpdate(spreadsheetId=spreadsheet_id,
                                                    body=append_request_body).execute()

  # Get the existing bandedRanges (if any)
  sheet_data = service.spreadsheets().get(spreadsheetId=spreadsheet_id).execute()
  our_sheet = None
  for sheet in sheet_data.get('sheets', []):
    if sheet['properties']['title'] == sheet_name:
      our_sheet = sheet
      break
  else:
    raise ValueError(f"Sheet '{sheet_name}' not found.")

  if our_sheet:
      print(json.dumps(our_sheet, indent=4))
      our_banded_range = our_sheet['bandedRanges']
      our_banded_range[0]['range']['endRowIndex'] += 1```