I'm not sure what "sticks" refers to inthe restaurant scene, but I'm quite sure that the example you found on the internet has nothing to do with it. There's no point looking for examples of the phrase "refilled and sticks" any more than it would make sense to pick the words "restaurant are changing" out of your description of the scene. Not every sequence of words is a meaningful phrase!
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khoff
.....or possibly there is some kind of "sticks" that the employee refilled in addition to refilling the sugar packs. Perhaps coffee stir sticks?
Many thanks khoff for your note. Yes, that is my guess too. I think that the sentence "Sugar packs refilled and sticks [stir sticks]" is just another way of saying "I refilled sugar packs in common with