Many years ago, air hostesses archetypally asked passengers
“Tea or coffee?”
The possible answers were
“No, (thank you)”
“(Yes), tea(, please)”
“(Yes), coffee(, please)”
In the last case, the air hostess would then ask
“Tea? Or coffee?”
This can also be written as “Tea or coffee?” but is distinguished by a rising intonation on “tea”, followed by a small pause, then a falling intonation on “coffee”, compared to an overall upward intonation for the first “Tea or coffee?”.
English grammar distinguishes polar (or yes/no) questions and alternative questions. The answers to “Do you want a hot drink?” are “Yes(, I want a hot drink)(, please)” and “No(, I don’t want a hot drink)(, thank you)”. Offering tea and coffee as a choice doesn’t fundamentally change that. Strictly speaking, the only two answers are “yes” and “no”. Answering “yes” is not non-cooperative; answering “yes, tea” or “yes, coffee” is cooperative, but not required.
On the other hand, the answers to “Do you want tea? or coffee (?)” are “Tea(, please)” and “Coffee(, please). Answering “Yes(, please)” is decidedly non-cooperative, and may result in a cup of coftea. (There are more choices; I found a 50-page academic paper titled Responding to alternative and polar questions. And less academically: