  Charmonium production is a probe sensitive to deconfinement in
nucleus-nucleus collisions. The production of J/$\psi$ via regeneration within
the QGP or at the phase boundary has been identified as an important ingredient
for the description of the observed J/$\psi$ nuclear modification factor at the
LHC. The $\psi(2S)$ production relative to J/$\psi$ is a possible discriminator
between the two regeneration scenarios. Studies of $\psi(2S)$ production in
central nucleus-nucleus collisions at low transverse momentum ($p_{\rm T}$) are
crucial, particularly at the LHC, where regeneration appears to be dominant. A
significant $\psi$(2S) signal is extracted at low $p_{\rm T}$ and forward
rapidity in the dimuon decay channel for the first time. This measurement
relies on the $\psi(2S)$ cross section measured recently in pp collisions at
$\sqrt{s_{\rm }}=5.02$ TeV with an unprecedented precision compared to previous
ALICE results. In this contribution, we present newly published results on the
$\psi(2S)$-to-J/$\psi$ ratio and the $\psi(2S)$ nuclear modification factor in
Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV. Results are reported as a
function of centrality and $p_{\rm T}$ for $p_{\rm T}<12$ GeV/c and are
compared to available NA50 and CMS measurements. Comparisons to transport and
statistical hadronization model predictions are also provided to shed light on
the charmonium states recombination mechanism
