Air pressure is about 10^5 Pa, I think, so that puts us somewhere down the bottom area of the liquid water phase. The story looks about the same up to around 10^8 Pa, so we can consider this area first.

I imagine it could be possible that excessive tightening of a threaded plug on a spherical enclosure or a steel water bottle could produce pressure in excess of 10^8 Pa, I haven't considered what might limit that.

Moving our shaky finger leftward on the phase diagram, we may discover ice Ih, hexagonal ice, the most well-known ice.

Ice densities are listed farther down the page. In an enclosed environment, density will be unable to change. So, I'm guessing that hexagonal ice won't be what happens. I guess we'd get stuck on that phase transition line, as pressure rose.