Do people honestly think Americans don't have rich social lives? Just because we socialize differently doesn't mean it isn't rich. Most Americans seem to prefer church groups, and small friend and family gatherings at their homes rather than going out and mingling in urban entertainment districts and bars.
Europeans get most of their perspective on US social living conditions from the terminally online, who are disproportionately likely to have no social life. The average American living in, say, the Midwest doesn't show up in the anecdotes that stereotypes are built around.
I'm an American and it definitely seems like we are in a significant and worsening loneliness crisis. I have no idea to what degree any of it is unique to Americans. Social connectedness, socialization rates, and companionship have all been declining for quite a while now. Lot's of potential causes and theories about it. [1] is a decent overview.
Like personally I'm doing great, and so are a lot of people I know, and I'm sure you as well. But I think a lot of Americans are struggling badly with their social lives.
#1 Reason is likely the urban fabric of places being non-walkable & car dependent. It's a physical structure that doesn't lead itself to spontaneity and new connections.
I recommend reading Robert Putnam's Bowling Alone (2000). American civic and social engagement has been declining in almost every measurable way for 50 years now. There is no way to deny this.
The largest contributor according the book's surveys and studies (and I love saying this) is television outcompeting in-person fun. Car dependency is a factor, but IIRC was factor #2 or #3. While this ranking was true at the time of publication, I would wager that time spent on "screens" is likely factor #1, #2, and #3 now.
I would wager that many people are fleeing their hometowns to socialize in cities not because they're walkable, but because the density of people increases, allowing you to have better odds meeting real humans who haven't been lost to the allure of the indoors.