  Relativistic hadronic plasmas can become under certain conditions
supercritical, abruptly and efficiently releasing the energy stored in protons
through photon outbursts. Past studies have tried to relate the features of
such hadronic supercriticalities (HSC) to the phenomenology of Gamma-Ray Burst
(GRB) prompt emission. In this work we investigate, for the first time, HSC in
adiabatically expanding sources. We examine the conditions required to trigger
HSC, study the role of expansion velocity, and discuss our results in relation
to GRB prompt emission. We find multi-pulse light curves from slowly expanding
regions ($u_{\rm exp}\lesssim 0.01 c)$ that are a manifestation of the natural
HSC quasi-periodicity, while single-pulse light curves with a fast rise and
slow decay are found for higher velocities. The formation of the photon
spectrum is governed by an in-source electromagnetic cascade. The peak photon
energy is $\sim 1$ MeV ($\sim 1$ GeV) for maximum proton energies $\sim 1-10$
PeV ($1-10$ EeV) assuming a jet Lorentz factor 100. Peak $\gamma$-ray
luminosities are in the range $10^{49}-10^{52}$ erg s$^{-1}$, with the
MeV-peaked spectra being $\sim 100-300$ times more luminous than their
GeV-peaked analogues. HSC bursts peaking in the MeV are also copious $\sim 10$
TeV neutrino emitters, with an all-flavour fluence $\sim 10\%$ of the
$\gamma$-ray one. The hypothesis that typical long-duration GRBs are powered by
HSC could be tested in the near future with more sensitive neutrino telescopes
like IceCube-Gen2.
