  In a view of recent proposals for the realization of anisotropic light-matter
interaction in such platforms as (i) non-stationary or inductively and
capacitively coupled superconducting qubits, (ii) atoms in crossed fields and
(iii) semiconductor heterostructures with spin-orbital interaction, the concept
of generalized Dicke model, where coupling strengths of rotating wave and
counter-rotating wave terms are unequal, has attracted great interest. For this
model, we study photon fluctuations in the critical region of
normal-to-superradiant phase transition when both the temperatures and numbers
of two-level systems are finite. In this case, the superradiant quantum phase
transition is changed to a fluctuational region in the phase diagram that
reveals two types of critical behaviors. These are regimes of Dicke model (with
discrete $\mathbb{Z}_2$ symmetry), and that of (anti-) and Tavis-Cummings
$U(1)$ models. We show that squeezing parameters of photon condensate in these
regimes show distinct temperature scalings. Besides, relative fluctuations of
photon number take universal values. We also find a temperature scales below
which one approaches zero-temperature quantum phase transition where quantum
fluctuations dominate. Our effective theory is provided by a non-Goldstone
functional for condensate mode and by Majorana representation of Pauli
operators. We also discuss Bethe ansatz solution for integrable $U(1)$ limits.
