You've done a good job of finding a few sources which seem to exclude water from being classified as a beverage. However, for every one dictionary entry you can find that excludes water, I can probably find one that specifically includes water. Some seem to allow for some wiggle room, wisely using a word like usually or sometimes, while others make no mention of water at all. The definition seems to be fluid.
Ultimately, though, this really depends on context.
Say we work for an airline, and we are trying to figure out which beverages we need to stock on each flight. We serve drinks like orange juice, Coca-Cola, and bottled water:
In this scenario, I would classify the water as a beverage, because, like the other beverages on the beverage cart, it's purchased by the airline in single-serving containers, and it's also dispensed from single-serving containers. It would be silly to exclude water from this beverage study – and even sillier to worry about the beverage study being mistitled because we happen to be including bottled water in the data.
However, let's say we were trying to figure out which beverages are consumed most at a particular airport. In that case, I would include ALL of the beverages sold at the newspaper stand – which we can see includes Perrier and some other bottled water:
but I would NOT include water taken from the water fountains, because the data would be too hard to collect. (Furthermore, it would be impossible to differentiate which water was dispensed for consumption, and which was being used for, say, brushing your teeth or rinsing out your mouth.)
In short, in these scenarios, I would classify bottled water as a beverage, but not tap water – even though it's obvious that both can be drunk for refreshment.
If I was doing a similar beverage study at a restaurant, would I count free water as a beverage? That depends on the purpose of my study: am I trying to calculate profit, or am I trying to figure out how many cups to buy? In the former case, I exclude water; in the latter, it gets included.
So, is water a beverage? Just like the dictionaries collectively imply – sometimes water clearly is, sometimes water clearly isn't, and sometimes it's hard to say:
As for your sentence:
Tea is the most consumed beverage after water.
I think beverage works just fine there, and I can't think of any better word to use. If the muddiness of water-as-a-beverage bothers you, you could write it this way:
Excluding water, tea is the most consumed beverage.