  In the third-generation (3G) gravitational-wave (GW) detector era, the
multi-messenger GW observation for binary neutron star (BNS) merger events can
exert great impacts on exploring the cosmic expansion history. In this work, we
comprehensively explore the potential of 3G GW standard siren observations in
cosmological parameter estimations by considering the 3G GW detectors and the
future short $\gamma$-ray burst (GRB) detector THESEUS-like telescope joint
observations. Based on the 10-year observation of different detection
strategies, we predict that the numbers of detectable GW-GRB events are
334--674 with the redshifts $z<3.5$ and the inclination angles
$\iota<15^{\circ}$. For the cosmological analysis, we consider the
$\Lambda$CDM, $w$CDM, $w_0w_a$CDM models, and interacting dark energy (IDE)
models. We find that GW can tightly constrain the Hubble constant with
precisions of $0.345\%-0.065\%$, but perform not well in constraining other
cosmological parameters. Fortunately, GW could effectively break the
cosmological parameter degeneracies generated by the mainstream EM
observations, CMB+BAO+SN (CBS). When combining the mock GW data with the CBS
data, CBS+GW can tightly constrain the equation of state of dark energy $w$
with a precision of 1.26\%, close to the standard of precision cosmology.
Meanwhile, the addition of GW to CBS could improve constraints on cosmological
parameters by $34.2\%-94.9\%$. In conclusion, GW standard siren observations
from 3G GW detectors could play a crucial role in helping solve the Hubble
tension and probe the fundamental nature of dark energy.
