From my experience, clubs are much more connected with the community in Europe. Where I'm from, you'd have sports clubs that offer different sports at different levels. In Germany you'll find a "Sportverein (SV), Fussballclub (FC), Turn- und Sportgemeinschaft (TSG), etc" in almost every town. If it's a generic club, they'll have many sports. Eintracht Frankfurt for instance has a Bundesliga football team but they also have amateur football teams, handball teams, hockey, etc. Towns often have more than one sports club so there connection to "your" club as well.
So there is a direct connection between your town and the sports club. It's the place where you sign your kid up to participate in team sports. Independent clubs aren't really a thing in Europe, for instance Bayern Munich is the team from Munich. They'll probably never be based in Berlin just because they're making them a better offer. Local clubs often have a long history, too. It's not uncommon for a local sports club to be over a hundred years old as well (TSG 1899 Hoffenheim, founded in 1899).
Clubs are heavily involved in their communities. They do a lot of charity and community work. Lots of players come through the club’s youth system, which usually contains a disproportionate number of local kids.
The history of the clubs and cities are intertwined. It’s just a massive cultural deal. Can’t properly explain it but the clubs are part of it people’s identity, which often they inherit from their parents.
In the UK most clubs are literally in the middle of a residential community. In many working-class towns they're the literal and emotional centre of the community - visible from all around and one of just a few unchanging social things shared across generations. People are very heavily invested into them.
I don't think that's it. For fans, whether you "belong" to a club has nothing to do with money. It more what city you were born in, what games did your parents take you to when you were young, what trading cards did you own when you were a child or who were your idols when you played football as a kid, things like that.
So there is a direct connection between your town and the sports club. It's the place where you sign your kid up to participate in team sports. Independent clubs aren't really a thing in Europe, for instance Bayern Munich is the team from Munich. They'll probably never be based in Berlin just because they're making them a better offer. Local clubs often have a long history, too. It's not uncommon for a local sports club to be over a hundred years old as well (TSG 1899 Hoffenheim, founded in 1899).