350 °F are 176 °C, which is well above the boiling point of water; Liquid water can not get hotter than 100 °C at 1 atm. However, gaseous water (Steam) can become much hotter.
The oven can only hold around 1 atm; at the point where it exceeds this pressure in the inside, the mixture of gases will stream out of it in the respective proportions.
So what will happen is that during the heating process, air will exit the oven. as more and more water evaporates, this air will contain more and more water (which you will probably see condensing above the oven) according to the increasing amount of gaseous water in the oven.
When the 350°F are reached and the water amount in the air will reach your 598 g/m³, there will be less air and water leaving the oven, as some of the water condenses back into the puddle on the tray, but as long as you keep the pressure constant by allowing the water to escape, this will be vanishingly less and most of it will escape the oven. As long as there is liquid water on the tray, this water will have 100 °C, the air/water mixture in the oven will have 350 °F and the amount of gaseous water in the oven will be around 598g/m³. The water molecules in the air will approximately have the same kinetic energy as the air molecules; as most of the air molecules are heavier, the water will be accordingly faster. This will increase the heat conductivity in the oven, heating the food faster; if you shove your sourdough into the oven, water will condense on its surface too, giving the energy which was used to evaporate the water (which is a lot compared to similar substances!) to the loaf and heating it even faster, yielding a delicious crust. Enjoy it ;)
Edit; The density of 598g/m³ seems to be the density of pure steam at 100°C. Due to thermal expansion, I would expect it to be less at 180°C.