WASHINGTON — Scenes from a mid-summer tennis tournament.A former world No. 1 who remains one of the biggest stars in the sport asks the owner of the event if he can help her hold a cookout on the first day of competition, so she can mingle with the fans that she doesn’t see enough at other events.A man faces a boy for whom he used to serve as a tennis big brother in the round of 16.The biggest local hero goes out in the first round on opening night, while the biggest star of the moment among the American men celebrates like he has made the Wimbledon semifinal after he survives a three-set scare with a qualifier and occasional practice partner.Some of that and plenty more happened this week in Rock Creek Park in northwest Washington, at a tournament that in recent years has found a sweet spot. It balances sports and socializing; accessibility and fanciness; intensity in the moment and a sense of freedom ahead of what’s coming down the pike in a few weeks, plus healthy doses of surprise that can help everyone through the dog days of summer.Why Naomi Osaka is having the best Wimbledon of her careerAva WallaceOn Sunday around 11 p.m., four-time Grand Slam champion Naomi Osaka texted Mark Ein, the Washingtonian entrepreneur and sports investor who owns the tournament, to ask whether he could set up a summer cookout. Osaka wanted to show some love to the people who had shown her plenty, at a rare event on the tennis circuit where she sees the crowd diversity she wishes she could see week in, week out.“There’s not much diversity on the tour, and when I came here yesterday — yesterday was my first time — I just saw so many beautiful Black women there. And they were all coming up to me and embracing me and I just felt so welcomed and loved,” Osaka said during an interview with Racquet Theory.Ein got some of the local food trucks he brought on site for the event to give away food for the cookout, and for an hour on a sultry Monday evening, Osaka chatted on a plaza near the entrance to the grounds where some version of this tournament has taken place for the past 53 years.No sponsor involved. No VIP ticket required. Just show up, grab a burger and chat with one of the biggest crossover sports stars in the world about tennis or motherhood or fashion or even the weather — which, in maybe the biggest surprise of all, turned crisp and clear and cool following a Noah’s Ark storm Tuesday night.