Some puppies just like to drink!
I've seen healthy puppies, that will drink whatever water you give them, it's like a habit.
If you have ruled out all medical things, including a UTI, I would try limiting his water intake. Give him water...but measure it out and give him a chance every hour or so to drink. Without water sitting out all of the time, he may just stop the excessive drinking...and it will be much easier to housetrain.
I've had a few puppies through the years that I boarded....that did the same thing...and I made my concerns known to the owners. After all sorts of tests...and worry...the owner's just had to control the access of water. Most common in Lab breeds....they just love to drink.
I'm hoping that you get some answers.
Gina