pdq,
"Water is continually being produced by the combination of hydrogen and oxygen atoms. Those atoms have never been combined before so the water molecule produced is new and unique."

That only happens when hydrogen, gas or in a compound, burns.
That does not have a signicant effect on the planet's water supply.
You remember the water cycle from school?
The same molecules of water just go round and round.
Your bottle contains molecules that have been drunk many times before.