I don't have a citation for loneliness per se, but suicide rates for young people are much higher in rural areas, "even after controlling for a broad array of county-level sociodemographic, economic, and health care system characteristics."

https://jamanetwork.com/journals/jamapediatrics/fullarticle/...

Of course, there's always the issue about whether suburbs and exurbs count as rural or urban, which leads to people talking past each other.

I can't see where they controlled for distance needed to travel to reach emergency departments after a suicide attempt. I'm sure they did, because it's a pretty big factor for how many people die from some methods, but it would have been nice to see this more clearly described.

Well, even if that accounts for part of the effect, it's still a benefit from urban living!

Urban living might be associated with mental illness, but so is poverty. Not because poverty causes mental illness, but because mental illness causes poverty. Mental illness also causes people to live in cities, because their needs are better met in cities.