  We investigate the stellar mass - black hole mass
($\mathcal{M}_*-\mathcal{M}_\mathrm{BH}$) relation with type 1 AGN down to
$\mathcal{M}_\mathrm{BH}=10^7 M_\odot$, corresponding to a $\simeq -21$
absolute magnitude in rest-frame ultraviolet (UV), at $z = 2-2.5$. Exploiting
the deep and large-area spectroscopic survey of the Hobby-Eberly Telescope Dark
Energy Experiment (HETDEX), we identify 66 type 1 AGN with
$\mathcal{M}_\mathrm{BH}$ ranging from $10^7$ to $10^{10} M_\odot$ that are
measured with single-epoch virial method using C{\sc iv} emission lines
detected in the HETDEX spectra. $\mathcal{M}_*$ of the host galaxies are
estimated from optical to near-infrared photometric data taken with Spitzer,
WISE, and ground-based 4-8m class telescopes by CIGALE SED fitting. We further
assess the validity of SED fitting in two cases by host-nuclear decomposition
performed through surface brightness profile fitting on spatially-resolved host
galaxies with JWST/NIRCam CEERS data. We obtain the
$\mathcal{M}_*-\mathcal{M}_\mathrm{BH}$ relation covering the unexplored
low-mass ranges of $\mathcal{M}_\mathrm{BH}~\sim~10^7-10^8~M_\odot$, and
conduct forward modelling to fully account for the selection biases and
observational uncertainties. The intrinsic
$\mathcal{M}_*-\mathcal{M}_\mathrm{BH}$ relation at $z\sim 2$ has a moderate
positive offset of $0.52\pm0.14$~dex from the local relation, suggestive of
more efficient black hole growth at higher redshift even in the low-mass regime
of $\mathcal{M}_\mathrm{BH}~\sim~10^7-10^8~M_\odot$. Our
$\mathcal{M}_*-\mathcal{M}_\mathrm{BH}$ relation is inconsistent with the
$\mathcal{M}_\mathrm{BH}$ suppression at the low-$\mathcal{M}_*$ regime
predicted by recent hydrodynamic simulations at a $98\%$ confidence level,
suggesting that feedback in the low-mass systems may be weaker than those
produced in hydrodynamic simulations.

Astrophysics of Galaxies