There are repeatibility concerns, e.g. see this article from the same journal as the original link posted here: https://doi.org/10.1177/0956797620916786 , but that's not what bothers me the most.
What bothers me is that FMRI only measures blood flow, and people get tricked into thinking it's reading minds or revealing personalities. It just measures blood flow -- not electrical signals, not neural architecture, not thought. Sure, if you map that in high res 4D you're going to get lots of data and when you have lots of data you can find lots of patterns. When you can find lots of patterns you can publish lots of papers and fund yourself.
If there is a significant effect here, the paper should at best be titled "Lonely individuals have blood going to slightly different parts of their brains than non-lonely individuals." Ok, maybe... so what? Is this going to lead to some breakthrough therapy? No, it's going to be used to build further castles in the air. It'll be cited in other FMRI studies.
I don't have medical training, but my experience publishing and reviewing papers in science gives me a strong gut feeling that this stuff is worthless other than as a way to amplify bias and mint papers.