I have no recent proof, though expect Asia originating flights to have soy milk instead of cow milk, since many Asian people are intolerant to cow milk (liability issue). The Brand: I think you'll get what is available at the caterer, so highly country depending.

Some 10 years ago, I asked upfront from Eva Air to load 0.5 L semi-skimmed milk for me (medical reasons). They complied with that, even loaded a full liter each leg and kept serving until finished (that's 500 kcal). They confirmed with me upfront, the milk might be soy milk, to which I agreed.

Edit: And on my LH CX flights, I do get "normal" milk with my tea, so it's definitely available, though I do not know about the qty.

Regarding HK style milk-tea: That's just "power" with water. Tastes OK, though for my liking usually a bit to much sweet.