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We present our sixth work in a series dedicated to variability studies of active galactic nuclei (AGN) based on the survey of the COSMOS field by the VLT Survey Telescope (VST). Its 54 r-band visits over 3.3 yr and single-visit depth of 24.6 r-band mag make this dataset a valuable scaled-down version that can help forecast the performance of the Rubin Observatory Legacy Survey of Space and Time (LSST). This work is centered on the analysis of the structure function (SF) of VST-COSMOS AGN, investigating possible differences in its shape and slope related to how the AGN were selected, and explores possible connections between the ensemble variability of AGN and black-hole mass, accretion rate, bolometric luminosity, redshift, and obscuration of the source. Given its features, our dataset opens up the exploration of samples ~2 mag fainter than most of the literature to date. We identify several samples of AGN - 677 in total - obtained by a variety of selection techniques which partly overlap. Our analysis compares results for the various samples. We split each sample in two based on the median of the physical property of interest, and analyze differences in the shape and slope of the SF, and possible causes. While the shape of the SF does not change with depth, it is highly affected by the type of AGN (unobscured/obscured) included in the sample. Where a linear region can be identified, we find that the variability amplitude anticorrelates with accretion rate and bolometric luminosity, consistent with previous literature on the topic, while no dependence on black-hole mass emerges from this study. With its longer baseline and denser and more regular sampling, the LSST will allow an improved characterization of the SF and its dependencies on the mentioned physical properties over much larger AGN samples.