Tuning cell shape by altering the biophysical properties of biomaterial substrates on which cells operate would provide a potential shape-driven pathway to control cell phenotype. However, there is an unexplored dimensional scale window of three-dimensional (3D) substrates with precisely tunable porous microarchitectures and geometrical feature sizes at the cell's operating length scales (10-100 μm). This paper demonstrates the fabrication of such high-fidelity fibrous substrates using a melt electrowriting (MEW) technique. This advanced manufacturing approach is biologically qualified with a metrology framework that models and classifies cell confinement states under various substrate dimensionalities and architectures. Using fibroblasts as a model cell system, the mechanosensing response of adherent cells is investigated as a function of variable substrate dimensionality (2D vs. 3D) and porous microarchitecture (randomly oriented, "non-woven" vs. precision-stacked, "woven"). Single-cell confinement states are modeled using confocal fluorescence microscopy in conjunction with an automated single-cell bioimage data analysis workflow that extracts quantitative metrics of the whole cell and sub-cellular focal adhesion protein features measured. The extracted multidimensional dataset is employed to train a machine learning algorithm to classify cell shape phenotypes. The results show that cells assume distinct confinement states that are enforced by the prescribed substrate dimensionalities and porous microarchitectures with the woven MEW substrates promoting the highest cell shape homogeneity compared to non-woven fibrous substrates. The technology platform established here constitutes a significant step towards the development of integrated additive manufacturing-metrology platforms for a wide range of applications including fundamental mechanobiology studies and 3D bioprinting of tissue constructs to yield specific biological designs qualified at the single-cell level.