  The generic phase diagram of lightly hole-doped high-$T_c$-cuprates hosts
antiferromagnetic insulating phase with well-defined spin-wave excitations.
Contrary to the weak-coupling prediction, these modes persist up to the
overdoped metallic regime as intense and dispersive paramagnons. Here we report
on our study of the low-energy magnetic and charge excitations within the
extended Hubbard model at strong-coupling, using a modified $1/N$ expansion
method with a variational state serving as the saddle point solution. Despite
clear separation of magnetic and Hubbard-$U$ energy scales, we find that
incipient Mottness affects qualitatively dispersions and widths of magnetic
modes throughout entire phase diagram. The obtained magnetic and charge
dynamical structure factors agree semi-quantitatively with recent resonant
$X$-ray and neutron scattering data for
$\mathrm{La_{2-\mathit{x}}Sr_\mathit{x}CuO_4}$ and
$\mathrm{(Bi,Pb)_2(Sr,La)_2CuO_{6+\delta}}$ at all available doping levels. The
weak-coupling random-phase-approximation fails already for underdoped samples,
pointing to the non-trivial intertwining of distinct energy scales in cuprate
superconductors. The existence of a discrete charge mode which splits off the
electron-hole continuum is also predicted.
