Aims: We present results from deep and very spatially extended CTIO/DECam g and r photometry (reaching out to 2 mag below the oldest main-sequence turn-off and covering 20 deg2) around the Sextans dwarf spheroidal galaxy. We aim to use this dataset to study the structural properties of Sextans overall stellar population and its member stars in different evolutionary phases, as well as to search for possible signs of tidal disturbance from the Milky Way, which would indicate departure from dynamical equilibrium. Methods: We performed the most accurate and quantitative structural analysis to-date of Sextans' stellar components by applying Bayesian Monte Carlo Markov chain methods to the individual stars' positions. Surface density maps are built by statistically decontaminating the sample through a matched filter analysis of the colour-magnitude diagram, and then analysed for departures from axisymmetry. Results: Sextans is found to be significantly less spatially extended and more centrally concentrated than early studies suggested. No statistically significant distortions or signs of tidal disturbances were found down to a surface brightness limit of 31.8 mag/arcsec2 in V-band. We identify an overdensity in the central regions that may correspond to previously reported kinematic substructure(s). In agreement with previous findings, old and metal-poor stars such as Blue Horizontal Branch stars cover a much larger area than stars in other evolutionary phases, and bright Blue Stragglers (BSs) are less spatially extended than faint ones. However, the different spatial distribution of bright and faint BSs appears consistent with the general age and metallicity gradients found in Sextans' stellar component. This is compatible with Sextans BSs having formed by evolution of binaries and not necessarily due to the presence of a central disrupted globular cluster, as suggested in the literature. We provide structural parameters for the various populations analysed and make publicly available the photometric catalogue of point-sources as well as a catalogue of literature spectroscopic measurements with updated membership probabilities. Full Tables 2 and 6 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/609/A53