efflorescence, can and will occur in almost all concrete given contact with water.
As it's the 'floor' that is showing the efflorescence at a crack (be it man made or naturally occurring) only suggests that there is moisture under the slab.
It's easier for efflorescence to form at a crack that goes all the way thru the slab than if there was no crack.
Given that it's on the floor just suggests it's damp under the slab. The only way to prevent it is to have had 6 mil plastic placed under the slab prior to construction.
And even then if there are bad enough water issues (like you had) the plastic barrier most likely wouldn't help either as it's only meant for dampness not flooding.
efflorescence forms when the moisture/dampness evaporates, (on the surface of the floor), so a proper coating placed over the concrete will stop efflorescence from forming.
Edit...cracks/cuts are trickier as the concrete expands and contracts at the crack/cut so a simple coating will most likely not seal this condition after it also cracks.
The crack/cut needs to be sealed by itself to prevent evaporation and the creation of efflorescence.
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