Google sheets (Apps Script) custom function to count cells with a given background color.

Code.gs

/**
 * Counts cell values in a range if they have the given background color
 * =countByColor("V16", "S12:W20")
 * 
 * @param  {String} Cell reference for color to compare as String.
 * @param  {String} Range to iterate through as String.
 * @return {int} Count of all cells matching background color.
 */
function countByColor(cellColorToCompare, rangeToCount) {
  var sheet = SpreadsheetApp.getActiveSpreadsheet();
  let color = sheet.getRange(cellColorToCompare).getBackgroundColor();
  let rangeToCheck = sheet.getRange(rangeToCount);

  var bgColors = rangeToCheck.getBackgrounds();
  let cols = rangeToCheck.getNumColumns();
  let rows = rangeToCheck.getNumRows();

  var cnt = 0;

  for (var i = 0; i < rows; i++) {
    for (var j = 0; j < cols; j++) {
      if (bgColors[i][j] == color) cnt++;
    }
  }

  return cnt;
}