  Constraints on the potential properties of superconducting cosmic strings
provide an indirect probe of physics beyond the standard model at energies
inaccessible to terrestrial particle colliders. In this study, we perform the
first joint Bayesian analysis to extract constraints on superconducting cosmic
strings from current 21-cm signal measurements while accounting rigorously for
the uncertainties in foregrounds and high redshift astrophysics. We include the
latest publicly available 21-cm power spectrum upper limits from HERA, 21-cm
global signal data from SARAS 3, and the synergistic probe of the unresolved
X-ray background in our final analysis. This paper thus constitutes the first
attempt to use 21-cm power spectrum data to probe cosmic strings. In contrast
to previous works, we find no strong constraints can be placed on
superconducting cosmic strings from current 21-cm measurements. This is because
of uncertainties in the X-ray emission efficiency of the first galaxies, with
X-ray emissivities greater than $3 \times 10^{40}$erg s$^{-1}$ M$_{\odot}^{-1}$
yr able to mask the presence of cosmic strings in the 21-cm signal. We conclude
by discussing the prospects for future constraints from definitive 21-cm signal
measurements and argue that the recently proposed soft photon heating should be
cause for optimism due to its potential to break degeneracies that would have
otherwise made the signatures of cosmic strings difficult to distinguish from
those of astrophysical origin.
