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Context: Stellar occultations, greatly enhanced by the publication of the Gaia data releases, permit not only the determination of asteroid size and shape, but also the retrieval of additional, accurate astrometry, with a possible relevant impact on the study of dynamical properties. The use of Gaia as reference catalogue and the recent implementation of an improved error model for occultation astrometry offer the opportunity to test its global astrometric performance on the existing data set of observed events, dominated by minor planets belonging to the main belt. Aims: We aim to explore the performance on orbit accuracy brought by reducing occultations by stellar positions given in Gaia Data Release 2 (DR2) and Early Data Release 3 (EDR3), exploited jointly with the new occultation error model. Our goal is to verify that the quality of DR2 and EDR3 provides a logical progression in the exploitation of occultation astrometry with respect to previous catalogues. We also want to compare the post-fit residuals to the error model. Methods: We began with accurate orbit adjustment to occultation data, either alone or joined to the other available ground-based observations. We then analyzed the orbit accuracy and the post-fit residuals. Results: Gaia EDR3 and DR2 bring a noticeable improvement to the accuracy of occultation data, bringing an average reduction of their residuals upon fitting an orbit of about a factor of 5 when compared to other catalogues. This is particularly visible when occultations alone are used, resulting in very good orbits for a large fraction of objects. We demonstrate that occultation astrometry can reach the performance of Gaia on small asteroids. The joint use of archival data and occultations remains more challenging due to the higher uncertainties and systematic errors of other data, mainly obtained by traditional CCD imaging.