There’s a difference between water and liquid.
Not sure if the solid core has more mass than the mantle.
In any case, I’d say it’s like a balloon with something solid floating in the middle.
I don’t believe the “solid” core is solid in any sense of the word we can relate to; kinda like how Jupiters volume is mostly gas, yet 99% of that is at densities greater than the Mariana trench — where you would vaporize, and would feel more solid to us that anything we’ve experienced — and the “solid” core is more like a molten hydrogen liquid; hotter than the surface of the sun (but not hot enough for fusion).