The Transiting Exoplanet Survey Satellite (TESS) mission has observed hundreds of millions of stars, substantially contributing to the available pool of high-precision photometric space data. Among them are the relatively rare gamma Doradus/delta Scuti (gamma Dor/delta Sct) hybrid pulsators, which have been previously studied using Kepler data. These stars are perfect laboratories to probe both inner and outer interior stellar layers thanks to them exhibiting both pressure and gravity modes. We seek to classify an all-sky sample of AF stars observed by TESS to find previously undiscovered hybrid pulsators and supply them in a catalogue of candidates. We also aim to compare the light curves produced with the TESS-Gaia Light Curve (TGLC) pipeline, currently underused in variability studies, with other publicly available light curves. We compared dominant and secondary frequencies of confirmed hybrid pulsators in Kepler, extended mission Quick Look Pipeline (QLP) data, and nominal and extended mission TGLC data. We then used a feature-based positive unlabelled (PU) learning classifier to search for new hybrid pulsators amongst TESS AF stars and investigated the properties of the detected populations. We find that the variability of confirmed hybrids in TGLC agrees well with the one occurring in QLP light curves and has a high recovery rate of Kepler-extracted frequencies. Our "smart binning" method allows for robust extraction of hybrids from large unlabelled datasets, with an average out-of-bag prediction for test set hybrids at 93.04%. The analysis of dominant frequencies in high-probability candidates shows that we find more pressure-mode dominant hybrids. Our catalogue includes 62 026 new candidate light curves from the nominal and extended TESS missions, with individual probabilities of being a hybrid in each available sector.