dry: food that has had no oil or moisture added to it
Both times this word describes food, it marks the absence of oil. In the instructions for the grain offering it is the plain alternative to a portion soaked in oil, and in the proverb it is bread eaten with nothing on it.
So the word signals plainness rather than thirst. A dry offering is not a defective one and a dry crust is still food. What the word says is that nothing rich has been added.
The proverb turns that plainness into a comparison: the barest food in a quiet house beats a table loaded with meat in a home full of quarreling. Hebrew has an ordinary adjective for dryness (יָבֵשׁ), used of withered plants and dry ground, and that one never carries this word's other meaning of a place in ruins.