  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 277-685
with the redshifts $z<4$ and the inclination angles $\iota<17^{\circ}$. For the
cosmological analysis, we consider five typical dark energy models, i.e., the
$\Lambda$CDM, $w$CDM, $w_0w_a$CDM models, and interacting dark energy (IDE)
models (I$\Lambda$CDM and I$w$CDM). We find that GW can tightly constrain the
Hubble constant with precisions of $0.09\%$-$0.37\%$, 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 parameter of dark
energy $w$ with a precision of $1.36\%$, close to the standard of precision
cosmology. Meanwhile, the addition of GW to CBS could improve constraints on
cosmological parameters by $35.3\%$-$92.0\%$. 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.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology