Fill the hole with air at 1atm & it’ll sit there very slowly evaporating though, same as it does on the ISS or on the surface of the earth. Gravity is irrelevant.
You don't seem to understand where that 1atm air pressure on the surface of the earth is coming from. Hint: on the surface of the Moon there is none.
In the ISS the air pressure is artificially kept at a certain level. To make a proper comparison, you should check what water would do outside of the ISS.
The context of my original comment was someone expecting that a cup of water at the centre of the earth would explode due directly to gravitational effects. This is wrong, as I pointed out.
Even on the surface of the earth it is the air pressure that prevents the water boiling off instantly, not gravity itself. On the surface of the earth that air pressure is due to the effect of gravity on the atmosphere, but you can supply that air pressure by a number of other means in other places. The air pressure inside the ISS is not there due to gravity after all! I suggest to you that if we can posit a hole at the centre of the earth, then we can fill it with air at 1atm if we want to - we are in the realm of mathematical models here, not reality after all :)