When you melt an ionic compound, do you "break" its electrostatic force of attraction, or its lattice energy?

I know that the melting point and the boiling point of ionic compounds are very high. However, when I was trying to find the reason for this, I found that this is because of the high electrostatic forces of attraction.

Does this mean that when we melt an ionic compound, we break its electrostatic forces? But then that means that in the liquid state, ionic compounds have only ions? That somehow doesn’t seem right to me. I tried to find out if its the lattice of the ions that we are breaking instead but found no clear answer.

So, that is my question. When melting an ionic compound, do we break its lattice or its electrostatic forces? what about boiling?

Edit: I got this from Wikipedia:

Even when the local structure and bonding of an ionic solid is disrupted sufficiently to melt it, there are still strong long-range electrostatic forces of attraction holding the liquid together and preventing ions boiling to form a gas phase.[65] This means that even room temperature ionic liquids have low vapour pressures, and require substantially higher temperatures to boil.[65] Boiling points exhibit similar trends to melting points in terms of the size of ions and strength of other interactions.[65] When vapourized, the ions are still not freed of one another. For example, in the vapour phase sodium chloride exists as diatomic "molecules".[66]

Here, the last point. "Sodium chloride, in the gas phase, exists as diatomic molecules." This means, the electrostatic forces of attraction between the ions don’t break ( The ions don’t get separated). Like, for NaCl, you still have "molecules" of NaCl, you don’t have ions of Na$^+$ and Cl$^-$ in the gas phase.

So, in a way, the only the lattice of NaCl broke, NaCl itself ( with the electrostatic forces) didn’t break.