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The Gaia mission discovered many new candidate \beta Cephei (\beta Cep) pulsators, which are meanwhile confirmed from TESS space photometry. We aim to analyse all currently available TESS data for these \beta Cep pulsators, of which 145 were new discoveries, in order to exploit their asteroseismic potential. \beta Cep stars belong to an under-represented class of pulsators in the current space photometry revolution while being of critical importance to improve evolution models of massive stars. We extracted light curves for 216 star from the TESS full-frame images and performed pre-whitening. Based on Gaia DR3, we deduced stellar properties and compared them to those of known \beta Cep stars. We developed a methodology to identify the dominant pulsation modes of the \beta Cep stars from Gaia and TESS amplitude ratios and from the detection of rotationally-split multiplets. We used grid modelling to gain insights into the population of \beta Cep stars. With the combination of TESS and Gaia, we successfully identified the mode degrees for 176 stars. of which the majority are dipole non-radial modes. Many non-radial modes show splittings in their TESS frequency spectra allowing us to assemble a large set of split multiplets in \beta Cep stars and to calculate their envelope rotation, spin parameter, and the level of differential envelope-to-surface rotation. For the latter, we find an upper limit of 4, with most stars rotating almost rigidly. We also provide the asymmetries of the multiplets. Based on grid modelling, we provide mass, convective core mass, and ages for 164 stars. By combining Gaia and TESS, we enable asteroseismology of \beta Cep stars as a population. Our study prepares for future detailed modelling based on individual frequencies of identified modes leading towards a better understanding of these massive pulsators, as crucial probes of stellar evolution theory. (abridged), Comment: Submitted to A&A on 30 July 2024