Point 1 above greatly understates the case. Water just sitting in a glass is constantly creating and destroying hydronium and hydroxide ions, and bare protons. Not to mention the carbon dioxide that gets dissolved as carbonic acid which can dissociate to bicarbonate.
On the other hand, its tough to talk about new water because under thermodynamics, all atoms of the same isotope at the same energy state are completely fungible, so it’s hard to say anything meaningful about the history of a molecule.