> HOAs don't make neighbors co-owners of your own property, do they?

Home-owner associations in Europe are frequently set up for apartment buildings, in which case, yes, the roof, foundation, hallways, stairwells, main piping, electricity, etc are all legally co-owned. Primary purpose of HOAs is to save for & plan long-term maintenance on the entire building.

HOAs for neighbourhoods, or blocks with single-family homes or terraced houses are pretty rare in Europe.