We present results of a Transiting Exoplanet Survey Satellite (TESS) search for short-period pulsations in compact stellar objects observed in years 1 and 3 of the TESS mission, during which the southern ecliptic hemisphere was targeted. We describe the TESS data used and the details of the search method. For many of the targets, we use unpublished spectroscopic observations to classify the objects. From the TESS photometry, we clearly identify 43 short-period hot-subdwarf pulsators, including 32 sdB stars, eight sdOB stars, two sdO stars, and, significantly, one He-sdOB star, which is the first of this kind to show short-period pulsations. Eight stars show signals at both low and high frequencies, and are therefore "hybrid" pulsators.We report the list of prewhitened frequencies and we show the amplitude spectra calculated from the TESS data. We make an attempt to identify possible multiplets caused by stellar rotation, and we select four candidates with rotation periods between 1 and 12.9d. The most interesting targets discovered in this survey should be observed throughout the remainder of the TESS mission and from the ground. Asteroseismic investigations of these data sets will be invaluable in revealing the interior structure of these stars and will boost our understanding of their evolutionary history. We find three additional new variable stars but their spectral and variability types remain to be constrained.