During three-dimensional (3D) bioprinting, the integration of living cells into hydrogel matrices results in complex biophysicochemical interactions between viscosity, shear stress, and temperature, critically influencing the structural and functional integrity of the resulting constructs. This study delves into the short-term biological ramifications of 3D extrusion printing of telomerase-immortalized human mesenchymal stromal cells (hMSC-TERT) embedded in bioinert hydrogels. Pluronic F127 and custom-synthesized poly(2-methyl-2-oxazoline)-block-poly(2-n-propyl-2-oxazine) (POx/POzi) are synthetic, block copolymers that create shear-thinning, physically crosslinked hydrogels that were used for this study. The rheological properties of the cell-free hydrogels and cell-laden bioinks were examined, revealing that they exhibited comparable behavior. Contrary to the original hypotheses, a key finding of this research is the reduction in cell viability (up to 50 %) within 24 h post-printing, a trend consistently observed across varying initial conditions. The relative expression levels of the mechanoresponsive genes FOS and PTGS2 were increased, partly due to the suspension and incubation of the cells in both hydrogels. Only FOS was significantly upregulated in some cases because of the printing process after 2 and 4 h of incubation. These insights highlight the potential of using POx/POzi hydrogel as a matrix in 3D bioprinting, particularly for depositing hMSC-TERT into structures with vasculature-mimicking scaffolds or scaffolds designed for bone regeneration.