  This study aims to assess the potential of the upcoming PLATO mission to
investigate exoplanet populations around stars in diverse Galactic
environments, specifically focusing on the Milky Way thin disk, thick disk, and
stellar halo. We aim to quantify PLATOs ability to detect planets in each
environment and determine how these observations could constrain planet
formation models. Beginning from the all-sky PLATO Input Catalog, we
kinematically classify the 2.4 million FGK stars into their respective Galactic
components. For the sub-sample of stars in the long-observation LOPS2 and LOPN1
PLATO fields, we estimate planet occurrence rates using the New Generation
Planet Population Synthesis (NGPPS) dataset. Combining these estimates with a
PLATO detection efficiency model, we predicted the expected planet yields for
each Galactic environment during a nominal 2+2 year mission. Based on our
analysis, PLATO is likely to detect at least 400 exoplanets around the
alpha-enriched thick disk stars. The majority of those planets are expected to
be Super-Earths and Sub-Neptunes with radii between 2 and 10 Earth radii and
orbital periods between 2 and 50 days, ideal for studying the link between the
radius valley and stellar chemistry. For the metal-poor halo, PLATO is likely
to detect between 1 and 80 planets with periods between 10 and 50 days,
depending on the potential existence of a metallicity threshold for planet
formation. The PLATO fields contain more than 3,400 potential target stars with
[Fe/H] < -0.6, which will help to improve our understanding of planets around
metal-poor stars. We identify a specific target list of 47 (kinematically
classified) halo stars in the high-priority, high-SNR PLATO P1 sample, offering
prime opportunities in the search for planets in metal-poor environments.
