The thing is that you wouldn't say "Guten Appetit" before drinking something, that expression is reserved for food.
"Prost" and "Prosit" as you used or "Zum Wohl" are appropriate.
Japanese Authors really need to stop this trope, it is getting predictable and boring. Grow up please Japan, and take a look at how relationships are handled in Manhwa.
@kwendy ; After the collapse of the Soviet Union and the Warsaw Pact it is gone, but honestly dude that you don't even know such basic stuff is worrying, that period still guides Polands modern decisions in term of militarization and politics.