Excel's "Highlight Duplicate Cells" is highlighting values which are actually different

Excel has a 15-digit limit to numerical precision, and as you've worked out your numbers have 16 so Excel is converting to a number and can't tell they're not duplicates (despite the fact you've marked them as text and put ' at the start of the numbers to signify a string).

One workaround is to concatenate a letter onto the column of strings you are testing for duplicates. As you can see here, by adding "a" on the front of your string Excel treats it as a real string.