The "over" in

  1. "... any water [that] the moon may have had to leak out into space over the 4.6 billion years that it has been in existence."

means = during the period of

OED:

over: 21. [...] for a period that includes.

This is not the same as the "over" in

  1. "The moon is over 4.6 billion years old."

OED

over: 13. In excess of, above, more than (a stated amount or number).