  We report the discovery of a hot ($T_{\rm eq}$ $\approx$ 1055 K) planet in
the small planet radius valley transiting the Sun-like star TOI-733, as part of
the KESPRINT follow-up program of TESS planets carried out with the HARPS
spectrograph. TESS photometry from sectors 9 and 36 yields an orbital period of
$P_{\rm orb}$ = $4.884765 _{ - 2.4e-5 } ^ { + 1.9e-5 }$ days and a radius of
$R_{\mathrm{p}}$ = $1.992 _{ - 0.090 } ^ { + 0.085 }$ $R_{\oplus}$.
Multi-dimensional Gaussian process modelling of the radial velocity
measurements from HARPS and activity indicators, gives a semi-amplitude of $K$
= $2.23 \pm 0.26 $ m s$^{-1}$, translating into a planet mass of
$M_{\mathrm{p}}$ = $5.72 _{ - 0.68 } ^ { + 0.70 }$ $M_{\oplus}$. These
parameters imply that the planet is of moderate density ($\rho_\mathrm{p}$ =
$3.98 _{ - 0.66 } ^ { + 0.77 }$ g cm$^{-3}$) and place it in the transition
region between rocky and volatile-rich planets with H/He-dominated envelopes on
the mass-radius diagram. Combining these with stellar parameters and
abundances, we calculate planet interior and atmosphere models, which in turn
suggest that TOI-733 b has a volatile-enriched, most likely secondary outer
envelope, and may represent a highly irradiated ocean world - one of only a few
such planets around G-type stars that are well-characterised.
