  TOI-1055 is a Sun-like star known to host a transiting Neptune-sized planet
on a 17.5-day orbit (TOI-1055 b). Radial velocity (RV) analyses carried out by
two independent groups using nearly the same set of HARPS spectra have provided
measurements of planetary masses that differ by $\sim$ 2$\sigma$. Our aim in
this work is to solve the inconsistency in the published planetary masses by
significantly extending the set of HARPS RV measurements and employing a new
analysis tool that is able to account and correct for stellar activity. Our
further aim was to improve the precision on measurements of the planetary
radius by observing two transits of the planet with the CHEOPS space telescope.
We fit a skew normal (SN) function to each cross correlation function extracted
from the HARPS spectra to obtain RV measurements and hyperparameters to be used
for the detrending. We evaluated the correlation changes of the hyperparameters
along the RV time series using the breakpoint technique. We performed a joint
photometric and RV analysis using a Markov chain Monte Carlo (MCMC) scheme to
simultaneously detrend the light curves and the RV time series. We firmly
detected the Keplerian signal of TOI-1055 b, deriving a planetary mass of
$M_b=20.4_{-2.5}^{+2.6} M_{\oplus}$ ($\sim$12%). This value is in agreement
with one of the two estimates in the literature, but it is significantly more
precise. Thanks to the TESS transit light curves combined with exquisite CHEOPS
photometry, we also derived a planetary radius of $R_b=3.490_{-0.064}^{+0.070}
R_{\oplus}$ ($\sim$1.9%). Our mass and radius measurements imply a mean density
of $\rho_b=2.65_{-0.35}^{+0.37}$ g cm$^{-3}$ ($\sim$14%). We further inferred
the planetary structure and found that TOI-1055 b is very likely to host a
substantial gas envelope with a mass of $0.41^{+0.34}_{-0.20}$ M$_\oplus$ and a
thickness of $1.05^{+0.30}_{-0.29}$ R$_\oplus$.
