I modified your code and it will count multiple colors on the Active Range or Highlighted Cells based on the code given.

function countColoredCells() {
  const activeRange = SpreadsheetApp.getActiveRange();
  const activeSheet = activeRange.getSheet();
  const formula = activeRange.getA1Notation()
  const range = activeSheet.getRange(formula);
  const bg = range.getBackgrounds();

  let count = {};
  for (let i = 0; i < bg.length; i++) {
    bg[i].forEach(x => {
      const findObject = Object.keys(count).find((y) => { return y == x });
      count[x] = findObject ? count[x] + 1 : 1;
    })
  }
  console.log(count);
  return count
}

Sample Colored Cells:

Note: Image is for visibility only.

Sample Output:

{ '#00ffff': 3,
  '#0000ff': 4,
  '#ff0000': 7,
  '#ffff00': 6,
  '#00ff00': 1 }

Reference:

• find()
• Objects