  The puzzling electronic correlation effects in the sodium cobaltate system
are studied by means of the combination of density functional theory and the
rotationally invariant slave boson (RISB) method in a cellular-cluster
approach. Realistic non-local correlations are hence described in the
short-range regime for finite Coulomb interactions on the underlying frustrated
triangular lattice. A local Hubbard U is sufficient to model the gross in-plane
magnetic behavior with doping x, namely antiferromagnetic correlations at
intermediate doping and the onset of ferromagnetic order above x>3/4 with a
mixed phase for 0.62<x<3/4. Important insight is thereby provided by the
occupations of local cluster multiplets retrieved from the RISB framework. The
extended modeling of the x$\ge$2/3 doping regime with an additional inter-site
Coulomb repulsion V on an experimentally verified effective kagom\'e lattice
allows to account for relevant charge-ordering physics. Therewith a fluctuating
charge-density-wave state with small quasiparticle weight and a maximum
in-plane magnetic susceptibility may be identified at x$\sim$3/4, just where
the magnetic ordering sets in.
