In November 2020, a new, bright object, eRASSt J234402.9-352640, was discovered in the second all-sky survey of SRG/eROSITA. The object brightened by a factor of at least 150 in 0.2-2.0 keV flux compared to an upper limit found six months previous, reaching an observed peak of 1.76-0.24+0.03 × 10-11 erg cm-2 s-1. The X-ray ignition is associated with a galaxy at z = 0.10, making the peak luminosity log10(L0.2-2keV/[erg s-1]) = 44.7 ± 0.1. Around the time of the rise in X-ray flux, the nucleus of the galaxy brightened by approximately 3 mag. in optical photometry, after correcting for the host contribution. We present X-ray follow-up data from Swift, XMM-Newton, and NICER, which reveal a very soft spectrum as well as strong 0.2-2.0 keV flux variability on multiple timescales. Optical spectra taken in the weeks after the ignition event show a blue continuum with broad, asymmetric Balmer emission lines, and high-ionisation ([OIII]λλ4959,5007) and low-ionisation ([NII]λ6585, [SII]λλ6716,6731) narrow emission lines. Following the peak in the optical light curve, the X-ray, UV, and optical photometry all show a rapid decline. The X-ray light curve shows a decrease in luminosity of ~0.45 over 33 days and the UV shows a drop of ~0.35 over the same period. eRASSt J234402.9-352640 also shows a brightening in the mid-infrared, likely powered by a dust echo of the luminous ignition. We find no evidence in Fermi-LAT γ-ray data for jet-like emission. The event displays characteristics of a tidal disruption event (TDE) as well as of an active galactic nucleus (AGN), complicating the classification of this transient. Based on the softness of the X-ray spectrum, the presence of high-ionisation optical emission lines, and the likely infrared echo, we find that a TDE within a turned-off AGN best matches our observations.