No question, Seattle U’s on campus gym is very small, not sure capacity but I believe it’s much smaller than gyms at Pepp / LMU /SMC. Similar to USF, they have a very compact, urban campus; difficult and expensive to expand or add on-campus facilities.
That said, they do play some of their hoops games at Climate Pledge Arena in Seattle, the recently substantially remodeled former Key Arena. Former home of the Supersonics and current home of WNBA Storm and NHL Kraken. Don’t know but I imagine Seattle U plays there as much as schedules permit.