  TOI-732 is an M dwarf hosting two transiting planets that are located on the
two opposite sides of the radius valley. By doubling the number of available
space-based observations and increasing the number of radial velocity (RV)
measurements, we aim at refining the parameters of TOI-732 b and c. We also use
the results to study the slope of the radius valley and the density valley for
a well-characterised sample of M-dwarf exoplanets. We performed a global MCMC
analysis by jointly modelling ground-based light curves and CHEOPS and TESS
observations, along with RV time series both taken from the literature and
obtained with the MAROON-X spectrograph. The slopes of the M-dwarf valleys were
quantified via a Support Vector Machine (SVM) procedure. TOI-732 b is an
ultrashort-period planet ($P\sim0.77$ d) with a radius
$R_b=1.325_{-0.058}^{+0.057}$ $R_{\oplus}$ and a mass $M_b=2.46\pm0.19$
$M_{\oplus}$ (mean density $\rho_b=5.8_{-0.8}^{+1.0}$ g cm$^{-3}$), while the
outer planet at $P\sim12.25$ d has $R_c=2.39_{-0.11}^{+0.10}$ $R_{\oplus}$,
$M_c=8.04_{-0.48}^{+0.50}$ $M_{\oplus}$, and thus $\rho_c=3.24_{-0.43}^{+0.55}$
g cm$^{-3}$. Also taking into account our interior structure calculations,
TOI-732 b is a super-Earth and TOI-732 c is a mini-Neptune. Following the SVM
approach, we quantified
$\mathrm{d}\log{R_{p,{\mathrm{valley}}}}/\mathrm{d}\log{P}=-0.065_{-0.013}^{+0.024}$,
which is flatter than for Sun-like stars. In line with former analyses, we note
that the radius valley for M-dwarf planets is more densely populated, and we
further quantify the slope of the density valley as
$\mathrm{d}\log{\hat{\rho}_{\mathrm{valley}}}/\mathrm{d}\log{P}=-0.02_{-0.04}^{+0.12}$.
Compared to FGK stars, the weaker dependence of the position of the radius
valley on the orbital period might indicate that the formation shapes the
radius valley around M dwarfs more strongly than the evolution mechanisms.
