Applying Kolmogorov-Smirnov (KS) test to evaluate multivariate synthetic tabular data (TVAE/TabDDPM vs. Empirical baseline)

I am benchmarking several tabular Generative AI models (including TVAE, TabDDPM, and WGAN-GP) to synthesize sensor data. I need to rigorously evaluate the statistical similarity between my generated synthetic datasets and the empirical baseline dataset.

I want to use the Two-Sample Kolmogorov-Smirnov test (scipy.stats.ks_2samp). However, my dataset is multivariate (consisting of features like Efficiency, Load, and Object Type). The standard KS test is designed for 1D distributions.

My question: What is the standard programmatic approach in Python to compute an aggregated KS score for a multidimensional tabular dataset?

Should I iterate through each continuous column independently, run ks_2samp, and average the p-values/statistics?

Or is there a specific library/method better suited for multivariate empirical cumulative distribution functions (eCDFs) in this context?

Thank you for your insights!