What does it mean when the construction clock shows for example, 4 hours ‘old’?

We already have an answer for a similar question which you can see here:
Can you please tell how the times work when waiting for gifts to open?

If you have more answers to add you can do that below.

What looks like "old" is actually "01d" (zero, one, d) meaning 1 day = 24 hours. So in your example, it is 4+24 = 28 hrs.