  Context. Hot subdwarfs experienced strong mass loss on the Red Giant Branch
(RGB) and are now hot and small He-burning objects. Aims. In this project we
aim to perform a transit survey in all available light curves of hot subdwarfs
from space-based telescopes (Kepler, K2, TESS, and CHEOPS), with our
custom-made pipeline SHERLOCK, in order to determine the occurrence rate of
planets around these stars, as a function of orbital period and planetary
radius. Methods. In this first paper, we perform injection-and-recovery tests
of synthetic transits for a selection of representative Kepler, K2 and TESS
light curves, to determine which transiting bodies, in terms of object radius
and orbital period, we will be able to detect with our tools. We also provide
such estimates for CHEOPS data, which we analyze with the pycheops package.
Results. Transiting objects with a radius $\lesssim$ 1.0 $R_{\Earth}$ can be
detected in most of Kepler, K2 and CHEOPS targets for the shortest orbital
periods (1 d and below), reaching values as small as $\sim$0.3 $R_{\Earth}$ in
the best cases. Reaching sub-Earth-sized bodies is achieved only for the
brightest TESS targets, and the ones observed during a significant number of
sectors. We also give a series of representative results for farther and bigger
planets, for which the performances strongly depend on the target magnitude,
the length and the quality of the data. Conclusions. The TESS sample will
provide the most important statistics for the global aim of measuring the
planet occurrence rate around hot subdwarfs. The Kepler, K2 and CHEOPS data
will allow us to search for planetary remnants, i.e. very close and small
(possibly disintegrating) objects, which would have partly survived the
engulfment in their red giant host.
