OK, sure. But TFA doesn't mention any coating.

I found a resource that corroborates what I said about behavior on water.[0] But it doesn't get into why that is.

And about density and electronegativity:

        g/cm^3   χ (Pauling)  1st ionization energy (kJ/mol)
   Li   0.535    0.98         520
   Na   0.968    0.93         496
   K    0.856    0.84         419

The difference in density is larger than that for electronegativity and 1st ionization energy. But yes, all three arguably play a role. Still, for Li vs Na, density seems like the major factor.

0) https://www.reference.com/science/alkali-metals-react-water-...