As far as college sports in Europe, I know something about this at least in the UK because I played on the soccer team at University College London for a year. UCL is a top 10 global university located in central London. Similar enrollment as Rutgers, but far more international students.
Of course college sports is bigger in the US than other countries, at least as measured by money and fan interest. On student participation, I'd say UCL beats out Rutgers. Approximately
70 sports are offered, including American football, baseball, and pole dancing.
The standard of competition is far below US division 1, with the exception of rowing and maybe field hockey. As for soccer, UCL currently fields 6 teams and had 7 when I was there. I played a few times for the first team and would judge the competition quality as in line with US division 1 soccer. Team was dominated by international students. English youngsters playing at that standard join pro clubs in their teens.
The only team sport with a pathway to a professional career was rugby. Not sure that is the case anymore because rugby had just gone professional then and today the rugby academy system is more sophisticated. Most professional rugby players, at least in Britain and Ireland, are college grads and today tend to balance college with rugby at a nearby pro team's academy.
Keep in mind far fewer resources are involved outside the US. At UCL, the sports are
run by a student taking a yearlong sabbatical and earning GBP 30,000, approximately USD 38,000. When I was playing soccer there, the team would bring 11 players and no coach, travel by public transit, and pay the referee a 2 pound coin each. That equated to about $70 then, or around $110 today. The assistant referees seemed by the referee's kids most of the time. Paid attendance was zero, maybe 5 or 10 spectators showed up.
The best part was UCL home field was at Arsenal's training ground at the time, Shenley.
No surprise coming to the US to be a student-athlete has great appeal to young international sportspeople, relative to the college sports opportunities outside the US.