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In the third-generation (3G) gravitational-wave (GW) detector era, themulti-messenger GW observation for binary neutron star (BNS) merger events canexert great impacts on exploring the cosmic expansion history. In this work, wecomprehensively explore the potential of 3G GW standard siren observations incosmological parameter estimations by considering the 3G GW detectors and thefuture short $\gamma$-ray burst (GRB) detector THESEUS-like telescope jointobservations. Based on the 10-year observation of different detectionstrategies, we predict that the numbers of detectable GW-GRB events are 277-685with the redshifts $z<4$ and the inclination angles $\iota<17^{\circ}$. For thecosmological 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 theHubble constant with precisions of $0.09\%$-$0.37\%$, but perform not well inconstraining other cosmological parameters. Fortunately, GW could effectivelybreak the cosmological parameter degeneracies generated by the mainstream EMobservations, CMB+BAO+SN (CBS). When combining the mock GW data with the CBSdata, CBS+GW can tightly constrain the equation of state parameter of darkenergy $w$ with a precision of $1.36\%$, close to the standard of precisioncosmology. Meanwhile, the addition of GW to CBS could improve constraints oncosmological parameters by $35.3\%$-$92.0\%$. In conclusion, GW standard sirenobservations from 3G GW detectors could play a crucial role in helping solvethe Hubble tension and probe the fundamental nature of dark energy.

A comprehensive forecast for cosmological parameter estimation using  joint observations of gravitational-wave standard sirens and short  $\gamma$-ray bursts