  Luminous Fast Blue Optical Transients (LFBOTs) are a class of extragalactic
transients notable for their rapid rise and fade times, blue colour and
accompanying luminous X-ray and radio emission. Only a handful have been
studied in detail since the prototypical example AT2018cow. Their origins are
currently unknown, but ongoing observations of previous and new events are
placing ever stronger constraints on their progenitors. We aim to put further
constraints on the LFBOT AT2023fhn, and LFBOTs as a class, using information
from the multi-wavelength transient light-curve, its host galaxy and local
environment. Our primary results are obtained by fitting galaxy models to the
spectral energy distribution of AT2023fhn's host and local environment, and by
modelling the radio light-curve of AT2023fhn as due to synchrotron
self-absorbed emission from an expanding blast-wave in the circumstellar
medium. We find that the neither the host galaxy nor circumstellar environment
of AT2023fhn are unusual compared with previous LFBOTs, but that AT2023fhn has
a much lower X-ray to ultraviolet luminosity ratio than previous events. We
argue that the variety in ultraviolet-optical to X-ray luminosity ratios among
LFBOTs is likely due to viewing angle differences, and that the diffuse, yet
young local environment of AT2023fhn - combined with a similar circumstellar
medium to previous events - favours a progenitor system containing a massive
star with strong winds. Plausible progenitor models in this interpretation
therefore include black hole/Wolf-Rayet mergers or failed supernovae.
