If a waiter is taking your order and asks, "How do you like your steak?", he is really asking, "How do you prefer that your steak be cooked?" And you can answer in one of these ways: "Very rare." "Rare." "Medium rare." "Medium." "Medium well done" "Well done." But if you have already begun to eat your steak, and the waiter passes by your table, and asks the same question, it now means, "Are you enjoying your steak?" And some possible answers are: "It's very tasty." "It's delicious." "The meat is very tender." "It's a bit tough." "It's as tough as shoe leather." "It's been overcooked." "How do you like steak?" means "do you enjoy eating steak?" Your suggested answer is perfect: "I like it a lot." I don't eat beef, so I would say, "I never eat steak."

You're correct, it's ambiguous. When he asks "How do you like your steak?" he is really asking "Do you want your steak grilled rare, medium, or well done?" But if he asked about something else, for example "How do you like your carrots?" then he is just asking "Do you you enjoy the taste of these carrots?" Steak is just an exception to the 'like' rules. Yes, if he said "How would you prefer your steak cooked?" that would remove the ambiguity.

A waiter would say, "How would you like your steak, sir?" The customer would reply, "Medium rare, please." (or however he likes it) That's it. Don't try other variations. Do not reinvent set patterns. You need to study more and invent less with English. Then you will save time, progress faster and not be confused.

Both how would you like your steak, and how do you prefer your steak are grammatically correct