M.E. is to my best knowledge often associated with leaky gut. Which is why there's such an emphasis on the gut. But much more promising and measured jak-inhibitors are already in the final stages of testing(upaciditinib, filgotinib). And if I recall correctly, trials on m.e. are already underway or at least funded for those drugs.
The study talked about in the article above. The JAK-Inhibitor Tofacitinib Rescues Human Intestinal Epithelial Cells and Colonoids from Cytokine-Induced Barrier Dysfunction Paywall, https://academic.oup.com/ibdjournal/advance-article-abstract/doi/10.1093/ibd/izz266/5637473 Sci hub, https://sci-hub.se/10.1093/ibd/izz266
Interestingly the drug, tofacitinib, is talked about in this paper. JAK/STAT Blockade Alters Synovial Bioenergetics, Mitochondrial Function, and Proinflammatory Mediators in Rheumatoid Arthritis Open access, https://onlinelibrary.wiley.com/doi/full/10.1002/art.40569