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 AT\,2018cow. 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 AT\,2023fhn, and LFBOTs as a class, using information from the multi-wavelength transient light curve, its host galaxy, and local environment. Our primary results were obtained by fitting galaxy models to the spectral energy distribution of AT\,2023fhn's host and local environment, and by modelling the radio light curve of AT\,2023fhn as due to synchrotron self-absorbed emission from an expanding blast wave in the circumstellar medium. We find that neither the host galaxy nor circumstellar environment of AT\,2023fhn are unusual compared with previous LFBOTs, but that AT\,2023fhn 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 AT\,2023fhn - 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 the mergers of black holes and Wolf-Rayet stars or failed supernovae.
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