The Mess Hall adds a boost to Officer stats as well as component tritanium efficiency, but the building is not locked to the Operations Level. Instead, it is linked to the sun of the officer level. The more officers you have promoted, the higher this building can be leveled up.
So, If your LVL35+, but your Officer Level is not 3000+, consider grinding on your officers and leveling them up.
Also, Hunting hostiles in Ty'Gokor (39) is one of the best places to gather Officer XP from PVE chests.