\begin{document}$\tilde{\chi}^{0}_2$\end{document} and \begin{document}$\tilde{\chi}^{\pm}_1$\end{document}. We categorize the annihilation processes into three main classes: \begin{document}$\tilde{\chi}_1^{\pm}$\end{document} coannihilation, Higgs funnel annihilation, and \begin{document}$\tilde{\tau}_1$\end{document} coannihilation. Each class combines interactions with \begin{document}$\tilde{\chi}_1^{\pm}$\end{document}. Our results indicate that achieving the correct relic density in heavier higgsino LSPs requires a combination of coannihilation and Higgs funnel mechanisms. We also assessed the potential of future experiments, such as XENONnT, LUX-ZEPLIN (LZ), PandaX-xT, and the Cherenkov Telescope Array (CTA), to probe these DM scenarios through direct and indirect detections. In particular, future spin-independent DM detections may cover all samples with the correct DM relic density for \begin{document}$\mu \gtrsim 1300$\end{document} GeV. Furthermore, future colliders such as the International Linear Collider (ILC) and Compact Linear Collider (CLIC) are expected to exceed the detection capabilities of current hadron colliders, especially for higher mass NLSPs. Notably, CLIC, which will operate at 3000 GeV, is anticipated to enable thorough investigation of all samples with insufficient DM relic density for \begin{document}$\mu \lesssim 1300$\end{document} GeV."> Investigating higgsino dark matter in the semi-constrained NMSSM -
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