How is the t-statistic value calculated in GEO2R or Bioconductor?
That is not trivial. GEO2R uses the Bayesian linear model-based framework limma https://bioconductor.org/packages/release/bioc/html/limma.html for the analysis. I doubt you can easily and meaningfully implement the relevant code in Python without a major effort and notable background knowledge. The user guide https://bioconductor.org/packages/release/bioc/vignettes/limma/inst/doc/usersguide.pdf has background information plus links to the relevant papers. Don't try to analyze things by hand, use expert software. If it is not significant, well, then it is not significant. A 2vs2 comparison is strongly underpowered, therefore lack of DEGs are not unexpected, especially for microarrays.