Hypersonic plasma jets generated by coaxial plasma guns are essential for plasma-jet-driven magneto-inertial fusion (PJMIF), and accurate electron-density diagnosticis is crucial for evaluating single-jet performance and providing benchmark data for plasma-liner formation. However, in the intermediate density range of 10^20–10^23\,\textm^-3, heterodyne laser interferometry (HLI) and Stark-broadening spectroscopy measure different physical quantities: the former gives a line-integrated density that requires geometrical reconstruction, whereas the latter provides an emission-weighted local density affected by line-shape fitting and instrumental deconvolution. This paper investigates the electron-density evolution of a hypersonic argon plasma jet produced by the ShanghaiTech Gun 1 (STG1) coaxial plasma gun by combining Mach-Zehnder HLI, optical emission spectroscopy (OES), photodiode-array time-of-flight measurements, and high-speed imaging. The interferometric phase shift at 532 nm is converted into line-integrated electron density, and the transverse jet size obtained from high-speed imaging is used to reconstruct the peak volumetric density with a Gaussian-profile model. Meanwhile, the Stark broadening of the \textm_\beta line at 486.1 nm is extracted through Voigt-profile deconvolution and used as an independent spectroscopic reference. Experimental results show that, for a representative shot, the interferometric phase shift averaged over the spectroscopic gate is approximately 1.20 rad, corresponding to a peak electron density of (1.60\pm0.11)\times10^22\;\textm^-3, while the \textm_\beta Stark-broadening method gives (1.22\;\pm 0.18)\times10^22\,\textm^-3 at the same time. Based on the cross-validated \textm_\beta density, an empirical calibration relation for the Ar II 480.6 nm line is further obtained as n_e=(7.64\times10^23)(\Delta\lambda_\textAr II-\Delta\lambda_\rmeff), where \Delta\lambda_\rmeff=2.42\times10^-3\,\textnm. Multi-shot statistics further indicate that the two diagnostics exhibit consistent temporal evolution and comparable density magnitudes, with a systematic difference of about 5–30% mainly caused by their different sampling meanings and spatial averaging effects. The measured density evolution shows a dominant main peak followed by a weaker secondary peak, suggesting that the jet density is influenced by the primary current-sheet acceleration and possibly by secondary compression or re-acceleration of residual plasma during the later discharge stage. This work establishes a cross-validated HLI-\textm_\beta-Ar II diagnostic framework, clarifies the applicability and limitations of different electron-density diagnostics, and provides reliable density data for future PJMIF jet-propagation and plasma-liner studies.