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The placing of the serving case in the galley indicates the location of the galley right next to the mess hall, placing the cooked meals into the serving case from inside the galley and taking them out of the serving case from inside the mess hall.
"Acquisition" is the only episode which canonically uses the term "serving case." The phrase "sliding cabinets" comes from the final draft scripts of "Acquisition" and "Regeneration". The serving cases were alternatively referred to as "food dispensers" in the final draft script of "Stigma".  The part of the mess hall they are depicted as being in was referred to as a "serving area" in the script of "Regeneration".
In the final draft script of "Singularity", Jonathan Archer was to have found that all the cases in the mess hall's "serving counter" were empty.  This scene isn't included in the final edit of "Singularity", though.
In the script of "Regeneration", Archer was to have taken a plate of food out of one of the serving cabinets, decided it didn't look appetizing, so opened another of the cabinets but decided the dish inside didn't look appetizing either, eventually settling on just a drink. In the final edit of the episode, however, he doesn't do exactly that, merely opening a single serving case, before deciding on having just a drink instead.