What would happen if we keep adding water to Earth? Earth would become massive, more surface area, and it can hold more water. Finally, would it collapse to a blackhole, or somehow water would be spilled into space?
Due to gravity, adding water produces heat via a process known as Kelvin-Helmholtz mechanism.
Once it reaches 65-350 $M_♃$ (Jupiter masses), so the earth bit is already a tiny dot in this huge ellipsoid, the earth doesn't matter now), if there is enough deuterium, it will start fusing deuterium, so it can technically be considered a brown dwarf.
After 350 $M_♃$, the heat produced by gravity should be enough to decompose enough water to the point it is able to sustain fusion and become a brown dwarf
After 1.5 $M_☉$ (solar masses) or 1500 $M_♃$, it will be able to start being a main sequence star.
If more water is added (and where my calculations get fuzzier), it should become a Giant, then a Hypergiant, then it'll collapse to a Neutron Star or Magnetar depending on how the water is added, then it would eventually collapse even more into a black hole.
If you keep adding water endlessly, at some point due to gravitational heat, the the water will be split into hydrogen and oxygen. So much of hydrogen, will make it into a star first. Then depending upon amount of hydrogen and age of the star, it may become a black hole, or a neutron star, or something else. There are many possibilities.