Transit least-squares survey IV. Earth-like transiting planets expected from the PLATO mission

In its long-duration observation phase, the PLATO satellite (scheduled for launch in 2026) will observe two independent, non-overlapping fields, nominally one in the northern hemisphere and one in the southern hemisphere, for a total of four years. The exact duration of each pointing will be determined two years before launch. Previous estimates of PLATO's yield of Earth-sized planets in the habitable zones (HZs) around solar-type stars ranged between 6 and 280. We use the PLATO Solar-like Light curve Simulator (PSLS) to simulate light curves with transiting planets around bright (m(V) <= 11) Sun-like stars at a cadence of 25 s, roughly representative of the >15 000 targets in PLATO's high-priority P1 sample (mostly F5-K7 dwarfs and subdwarfs). Our study includes light curves generated from synchronous observations of 6, 12, 18, and 24 of PLATO's 12 cm aperture cameras over both 2 and 3yr of continuous observations. Automated detrending is done with the Wotan software, and post-detrending transit detection is performed with the transit least-squares (TLS) algorithm. Light curves combined from 24 cameras yield true positive rates (TPRs) near unity for planets >= 1.2 R-circle plus with two transits. If a third transit is in the light curve, planets as small as 1 R-circle plus are recovered with TPR similar to 100%. We scale the TPRs with the expected number of stars in the P1 sample and with modern estimates of the exoplanet occurrence rates and predict the detection of planets with 0.5 R-circle plus <= R-p <= 1.5 R-circle plus in the HZs around F5-K7 dwarf stars. For the long-duration observation phase (2yr + 2yr) strategy we predict 11-34 detections, and for the (3 yr + 1 yr) strategy we predict 8-25 discoveries. These estimates neglect exoplanets with monotransits, serendipitous detections in stellar samples P2-P5, a dedicated removal of systematic effects, and a possible bias of the P1 sample toward brighter stars and high camera coverage due to noise requirements. As an opposite effect, Earth-sized planets might typically exhibit transits around P1 sample stars shallower than we have assumed since the P1 sample will be skewed toward spectral types earlier than the Sun-like stars assumed in our simulations. Moreover, our study of the effects of stellar variability on shallow transits of Earth-like planets illustrates that our estimates of PLATO's planet yield, which we derive using a photometrically quiet star similar to the Sun, must be seen as upper limits. In conclusion, PLATO's detection of about a dozen Earth-sized planets in the HZs around solar-type stars will mean a major contribution to this as yet poorly sampled part of the exoplanet parameter space with Earth-like planets.