  Aims. Gaia DR3 GSP-Phot and GSP-Spec parameters of known K- and M-type stars
with luminosity class I are examined and compared with parameters collected
from the literature, to assess their accuracy and their potential for stellar
classification of unknown intrinsically bright late-types. Gaia DR3 GSP-Phot
and GSP-Spec parameters were generated by the Astrophysical Parameters
Inference Software (Apsis). Methods. In the Gaia DR3 catalog, there are about
40,000 entries with Apsis parameters similar to those of known red supergiants,
RSGs, good parallaxes, and infrared 2MASS and WISE data. By using parallactic
distances, infrared photometry, and variability information, only 203 new
entries are found with luminosities and temperatures similar to that of known
RSGs and G-band amplitudes smaller than 0.5 mag. Their low-resolution BP/RP
spectra are compared with an empirically made spectral library of BP/RP spectra
of known bright late-type stars (C-rich, S-type, O-rich asymptotic giant branch
stars (AGBs), and RSGs) to obtain their spectral types. Results. Among them, 15
S-type stars are identified by peculiar absorption features due to ZrO and LaO
visible in their BP/RP spectra, one S/C star, and nine C-rich stars by their
strong CN absorption bands. K- and M-types can be reproduced with an accuracy
of two subtypes. 20 new RSGs are confirmed, of which six have bolometric
magnitudes brighter than those of the AGB limit: 2MASS J21015501+4517205, 2MASS
J16291280-4956384, 2MASS J10192621-5818105, 2MASS J20230860+3651450, 2MASS
J17084131-4026595, and 2MASS J16490055-4217328. The flag for C-rich stars of
the Gaia DR3 LPV pipeline is erroneously true for some RSGs and a visual
inspection of the BP/RP spectra is mandatory.
