MIT Mystery Hunt 2020/Espresso Stand

Espresso Stand is a wordplay puzzle from the round of the 2020 MIT Mystery Hunt.

Puzzle Elements
Flavortext - ''The names look right but the drink shorthand looks off. What does this barista need?''

One-File Wonder - Besides the flavortext, the only other object in this puzzle is a picture of a Starbucks order featuring seven drinks.

Identification (Food & Drink) - Indeed, the first step is determining what drinks were ordered; these can be inferred from the labels or directly looked up on the menu.

Error Correction - In doing so, however, one should quickly realize that the labels are wrong—they each refer to a different drink in the order!

Reordering - These references form a cycle, creating an ordering.

Mangled Clues - The "drink shorthand" doesn't seem all that indicative of actual shorthand—many words drop the usually-kept first letter. Instead, they're generated in a manner reflective of mangled clues: a function is applied to every word in the name. Applying this function to the name on the correct drink yields a bigram; ordering all seven using the cycle yields the answer.