Context. The Galactic magnetar SGR 1935+2154 has exhibited prolific high-energy (HE) bursting activity in recent years. Aims. Investigating its potential tera-electronvolt counterpart could provide insights into the underlying mechanisms of magnetar emission and very high-energy (VHE) processes in extreme astrophysical environments. We aim to search for a possible tera-electronvolt counterpart to both its persistent and sub-second-scale burst emission. Methods. We analysed over 25 hour of observations from the Large-Sized Telescope prototype (LST−1) of the Cherenkov Telescope Array Observatory (CTAO) during periods of HE activity from SGR 1935+2154 in 2021 and 2022 to search for persistent emission. For bursting emission, we selected and analysed nine 0.1 s time windows centred around known short X-ray bursts, targeting potential sub-second-scale tera-electronvolt counterparts in a low-photon-statistics regime. Results. While no persistent or bursting emission was detected in our search, we establish upper limits for the tera-electronvolt emission of a short magnetar burst simultaneous to its soft gamma-ray flux. Specifically, for the brightest burst in our sample, the ratio between tera-electronvolt and X-ray flux is ≲10−3. Conclusions. The non-detection of either persistent or bursting tera-electronvolt emission from SGR 1935+2154 suggests that if such components exist, they may occur under specific conditions not covered by our observations. This aligns with theoretical predictions of VHE components in magnetar-powered fast radio bursts and the detection of MeV─GeV emission in giant magnetar flares. These findings underscore the potential of magnetars, fast radio bursts, and other fast transients as promising candidates for future observations in the low-photon-statistics regime with Imaging Atmospheric Cherenkov Telescopes, particularly with the CTAO.