Hot subdwarf B (sdB) stars are post-main-sequence stars of high temperature and gravity. Approximately 30$\%$ of sdBs exhibit stable pressure and/or gravity-mode pulsations, which can be used via the timing method to test for companion stars and determine their orbital solutions. We used short cadence data from the Transiting Exoplanet Survey Satellite (TESS) to search for previously undiscovered companions to sdBs. In this paper, we focus on searching for companions with orbital periods shorter than 13.5$\,$d which are detectable within one sector of TESS data (about 27$\,d$). The timing method requires that we derive pulsation frequencies in subsets of data significantly shorter than the periods we are searching for, which we set at 0.5 to 1.5$\,$d. We investigated ten sdB stars with previously detected p-mode pulsations for which at least one p-mode pulsation remains detectable with a signal-to-noise ratio (S/N) $>$ 4 within data subsets of duration 0.5 - 1.5$\,$d. We find that two (TIC$\,$202354658 and TIC$\,$69298924) of these ten sdB stars likely have white dwarf companions and set limits on companion masses for the other eight sdB stars.

We present an update on the variable star survey performed on the TESS 30 min Full Frame Image (FFI) data reported by our first two papers in this series. This update includes a contamination analysis in order to identify false positives and analysis of the TESS 10 min FFI data collected during Years 3 and 4 of the mission. We clarify the variability status of 2 995 targets identifying 1 403 variable stars. In addition, we spectroscopically classify 24 pre-filtered targets sampled with the 10 min FFI data and discover 11 new sdB pulsators. Future follow-up space- and/or ground-based data of variables reported here, to identify the nature of their variability and reveal spectroscopic parameters of the stars, would complement this work.