Rather than a meta-analysis, I think a large direct study is better: https://www.sciencedirect.com/science/article/pii/S0191886920302555
It finds that yes, there is an effect, but it's modest. (As does the meta-analysis you linked.)
But both of those find that men are lonelier than women! So why do you say it "found the same stats"?
Jude says, and I quote, "In fact, as per this report, women are lonelier than men." Jude correctly conveyed the numbers from the report (57 vs 59%), but did not correctly convey the sentiment ("about the same") or the stated error (+-2%).
The meta-analysis you linked says, and I quote, "we found a close-to-zero mean effect of g = 0.08 (SE = 0.03, 95% CI [0.02, 0.13]). Although the size of the overall effect is small, it is statistically significant at the .05 significance level, p = .005, suggesting that males are slightly lonelier than females"
And the BBC survey I linked concurs, and finds a similar effect size: men are lonelier than women (but not that much).
So--what gives? The other studies are not radically at odds with what Jude says, but it certainly doesn't agree with him fully.
Additionally, given that practically no men have commented saying that Jude's treated the issue well, I'm not sure what your basis is for saying that he "handled it with sensitivity".
Phrases like, "“Male loneliness,” as we have been discussing it, isn’t real." are incredibly insensitive. It goes out of its way to state, "Male loneliness isn't real" with a caveat to make it technically true. But the implication still comes across like a slap in the face for anyone who cares to be sensitive about phrasings.
I do think Jude has called the "epidemic of male loneliness isn't a good summary of what's going on" thing correctly.
But he's wrong on details, and short on sensitivity.