Lack of high-precision long-term continuous photometric data for large samples of stars has prevented the large-scale exploration of pulsational variability in the OB star regime. As a result, the candidates for in-depth asteroseismic modelling remained limited to a few tens of dwarfs. The TESS nominal space mission has surveyed the southern sky, yielding continuous data of at least 27 d for hundreds of OB stars. We aim to couple TESS data in the southern sky with spectroscopy to study the variability over mass and evolution. We focus mainly on the presence of coherent pulsation modes that may or may not be present in the theoretical instability domains and unravel all frequency behaviour in the amplitude spectra of the TESS data. We compose a sample of 98 OB-type stars observed by TESS in Sectors 1-13 and with available high-resolution spectroscopy gathered by the IACOB and OWN surveys. We present the short-cadence 2-min light curves of dozens of OB-type stars, that have one or more spectra in the IACOB or OWN database. Based on these light curves and their Lomb-Scargle periodograms we perform variability classification and frequency analysis, and place the stars in the spectroscopic Hertzsprung-Russell diagram to interpret the variability in an evolutionary context. We deduce diverse origins of the variability found in all of the 98 OB stars in the TESS data. Among these we find several new variable stars, including three hybrid pulsators, three eclipsing binaries, high frequency modes in a Be star, and potential heat-driven pulsations in two Oe stars. We identify stars for which future asteroseismic modelling is possible, provided mode identification is achieved. By comparing the position of the variables to theoretical instability strips we discuss the current shortcomings in non-adiabatic pulsation theory, and the distribution of pulsators in the upper Hertzsprung-Russell diagram.
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