  We observe an enhanced stellar wind mass-loss rate from low-mass stars
exhibiting higher X-ray flux. This trend, however, does not align with the Sun,
where no evident correlation between X-ray flux and mass-loss rate is present.
To reconcile these observations, we propose a hybrid model for the stellar wind
from solar-type stars, incorporating both Alfv\'en wave dynamics and flux
emergence-driven interchange reconnection, an increasingly studied concept
guided by the latest heliospheric observations. For establishing a mass-loss
rate scaling law, we perform a series of magnetohydrodynamic simulations across
varied magnetic activities. Through a parameter survey concerning the surface
(unsigned) magnetic flux ($\Phi^{\rm surf}$) and the open-to-surface magnetic
flux ratio ($\xi^{\rm open} = \Phi^{\rm open}/\Phi^{\rm surf}$), we derive a
scaling law of the mass-loss rate given by $\dot{M}_w/\dot{M}_{w,\odot} =
\left( \Phi^{\rm surf} / \Phi^{\rm surf}_\odot \right)^{0.52}\left( \xi^{\rm
open} / \xi^{\rm open}_\odot \right)^{0.86}$, where $\dot{M}_{w,\odot} = 2.0
\times 10^{-14} \ M_\odot {\rm \ yr}^{-1}$, $\Phi^{\rm surf}_\odot = 3.0 \times
10^{23} {\rm \ Mx}$, and $\xi^{\rm open}_\odot = 0.2$. By comparing cases with
and without flux emergence, we find that the increase in the mass-loss rate
with the surface magnetic flux can be attributed to the influence of flux
emergence. Our scaling law demonstrates an agreement with solar wind
observations spanning 40 years, exhibiting superior performance when compared
to X-ray-based estimations. Our findings suggest that flux emergence may play a
significant role in the stellar winds of low-mass stars, particularly those
originating from magnetically active stars.
