It has nothing to do with the effort made in preparing food. The rishonim (mentioned by the Tur in the above siman) say it is gaavah to eat before davening, and therefore it is allowed to drink water, tea, coffee because it isn’t gaavah…
Many teshuvos have been written about drinking coffee with milk. Rav moshe has a heter because in our time, it’s so typical to drink it with milk and sugar that it’s not gaavah, but others disagreed. The prevailing custom is to drink coffee with milk and sugar.
However a fancy starbucks type drink would definitely be assur.
The poskim make no mention of the effort required in preparing the food, nor do they talk at all about missing davening.
Missing davening applies to mincha and maariv, as shu”a paskens.