Our DM makes us greet with an “open ended food offer” so something like “hi welcome to Starbucks, what can I get you for breakfast this morning?”

The speech is likely to engage in customer connections and upsell, as well as stall the car so your baristas can keep the window times as low as possible

That's a weird way of enforcing "customer connection" . At my store we just say "hi, good morning/afternoon/ evening... How are you doing today?... *Maybe small talk*.. Well, can we start you off with any food today?"
We usually don't ask their name unless they've come by several times. (Bc it's drive thru and people arent usually regulars.)
Also, asking for their name is usually for cafe to names on orders. At drive you don't really need it.

Lmao my SM would be down if I was like. What up? What can I make for ya? Or. Gooooooood eveEeNning like dracula

At my store we do the same thing “hey this is y/n welcome to Starbucks what can I get started for you today?” And if they order a food item like a breakfast sandwich we say “ would you like any siracha or avocado spread on the side for that?” And we always offer cake pops 🤷‍♀️🤷‍♀️

My manager just said be casual with them some thing like "hi welcome to Starbucks what are we making for you today"