  We investigate the fluctuations of the nodal number (count of the phase
singularities) in a natural extension of the well-known complex planar Berry
Random Wave Model - Berry (2002) - obtained by considering two independent real
Berry Random Waves, with distinct energies $E_1, E_2 \to \infty$ (at possibly
$\neq$ speeds). Our framework relaxes the conditions used in Nourdin, Peccati
and Rossi (2019) where the energies were assumed to be identical ($E_1 \equiv
E_2$). We establish the asymptotic equivalence of the nodal number with its
4-th chaotic projection and prove quantitative Central Limit Theorems (CLTs) in
the 1-Wasserstein distance for the univariate and multivariate scenarios. We
provide a corresponding qualitative theorem on the convergence to the White
Noise in a sense of random distributions. We compute the exact formula for the
asymptotic variance of the nodal number with exact constants depending on the
choice of the subsequence. We provide a simple and complete characterisation of
this dependency through introduction of the three asymptotic parameters:
$r^{log}$, $r$, $r^{exp}$. The corresponding claims in the one-energy model
were established in Nourdin, Peccati and Rossi (2019), Peccati and Vidotto
(2020), Notarnicola, Peccati and Vidotto (2023), and we recover them as a
special case of our results. Moreover, we establish full-correlations with
polyspectra, which are analogues of the full-correlation with tri-spectrum that
was previously observed for the nodal length in Vidotto (2021).
