Yeah, never said у мене є спрага in my life :) We always just say "Я хочу пити".
In English "I want to drink" does not imply "I am thirsty" because, I think, people don't say "I want to drink"! You can say "I want to drink something" which indeed doesn't imply that you are genuinely thirsty. In Ukrainian that would be "Я хочу чогось випити" which does not imply "Я хочу пити"
I believe Jake is correct. Even though word-for-word translation is 'I want to drink' , in English-speaking world 'I am thirsty' is much more prevalent and widely used in my experience. Also Ukrainians don't really say 'у мене спрага' (I have thirst) or 'я спраглий' (I am thirsty) all that often in everyday language.
A drink as a noun is напій. In principle, literally translating would give Я хочу напій, but this is not a common way to say it.
If it's about alcohol I'd go with (Я) хочу чогось випити (I want to drink something). In general case would be Я хочу якийсь напій (I want some drink).
Since we don't have articles, the feeling of "a" in "a drink" has to be emphasized by some other word like якийсь ("some")
I have read through the comments and understand that this is how you would say I am thirsty, but when learning a language wouldnt it be better to get more verbatum translations? Without going through this confusing comment section, one might not understand the difference between the word for thirsty and the word for to drink.
If you want to translate an Italian sentence "ho fame", you will say "I'm hungry" rather than "I have hunger". Same here. In Ukrainian there is no other way to say "I'm thirsty" apart from "I want to drink". These two can be freely translated into each other, since it's an expression rather than literal statement word by word.