Context. HR 10 has only recently been identified as a binary system. Previously thought to be an A-type shell star, it appears that both components are fast-rotating A-type stars, each presenting a circumstellar envelope. Although showing complex photometric variability, spectroscopic observations of the metallic absorption lines reveal variation explained by the binarity, but not indicative of debris-disc inhomogeneities or sublimating exocomets. On the other hand, the properties of the two stars make them potential δ Scuti pulsators. Aims. The system has been observed in two sectors by the TESS satellite, and was the target of three observing visits by CHEOPS. Thanks to these new data, we aim to further characterise the stellar properties of the two components. In particular, we aim to decipher the extent to which the photometric variability can be attributed to a stellar origin. In complement, we searched in the lightcurves for transient-type events that could reveal debris discs or exocomets. Methods. We analysed the photometric variability of both the TESS and CHEOPS datasets in detail. We first performed a frequency analysis to identify and list all the periodic signals that may be related to stellar oscillations or surface variability. The signals identified as resulting from the stellar variability were then removed from the lightcurves in order to search for transient events in the residuals. Results. We report the detection of δ Scuti pulsations in both the TESS and CHEOPS data, but we cannot definitively identify which of the components is the pulsating star. In both datasets, we find flicker noise with the characteristics of a stellar granulation signal. However, it remains difficult to firmly attribute it to actual stellar granulation from convection, given the very thin surface convective zones predicted for both stars. Finally, we report probable detection of transient events in the CHEOPS data, without clear evidence of their origin.