  Fast radio bursts (FRBs) are energetic, millisecond-duration radio pulses
observed at extragalactic distances and whose origins are still a subject of
heated debate. A fraction of the FRB population have shown repeating bursts,
however it's still unclear whether these represent a distinct class of sources.
We investigated the bursting behaviour of FRB 20220912A, one of the most active
repeating FRBs known thus far. In particular, we focused on its burst energy
distribution, linked to the source energetics, and its emission spectrum, with
the latter directly related to the underlying emission mechanism. We monitored
FRB 20220912A at $408$ MHz with the Northern Cross radio telescope and at $1.4$
GHz using the $32$-m Medicina Grueff radio telescope. Additionally, we
conducted $1.2$ GHz observations taken with the upgraded Giant Meter Wave Radio
Telescope (uGMRT) searching for a persistent radio source coincident with FRB
20220912A, which included high energy observations in the $0.3-10$ keV,
$0.4-100$ MeV and $0.03-30$ GeV energy range. We report $16$ new bursts from
FRB 20220912A at $408$ MHz during the period between October 16$^{\rm th}$ 2022
and December 31$^{\rm st}$ 2023. Their cumulative spectral energy distribution
follows a power law with slope $\alpha_E = -1.3 \pm 0.2$ and we measured a
repetition rate of $0.19 \pm 0.03$ hr$^{-1}$ for bursts having a fluence of
$\mathcal{F} \geq 17$ Jy ms. Furthermore, we report no detections at 1.4 GHz
for $\mathcal{F} \geq 20$ Jy ms. These non-detections imply an upper limit of
$\beta < -2.3$, with $\beta$ being the $408$ MHz $-$ $1.4$ GHz spectral index
of FRB 20220912A. This is inconsistent with positive $\beta$ values found for
the only two known cases in which an FRB has been detected in separate spectral
bands. We find that FRB 20220912A shows a decline of four orders of magnitude
in its bursting activity at $1.4$ GHz over a .. (abridged)
