Suggestion for 4 nights, 40 miles in Sierras in July

I doubt you'll get 40 miles in Twenty Lakes.

A loop through Dinkey Lakes and beyond into John Muir Wilderness, or from Kearsarge to Cottonwood or New Army and out at Horseshoe with help from a shuttle service, depending on you solitude vs tolerance of crowds preference.

Twenty Lakes gets really, really crowded.

Thanks so much Lori! We would like to avoid crowds, I know before Saddlebag it's quite crowded. Open to other suggestions around 30-40 miles if you have anything in mind, would love to take a look!

Enter horseshoe meadows and swing around the back side to whitney, then out the portal. You'll mostly be alone until Guitar lake and can do whitney/mt muir while there. I believe this is about 30-40 miles.

Is Virginia Lakes. The trailhead there will take you up over Virginia Lakes Pass, and you can explore Virginia Canyon, McCabe Lakes…wonderful area. And you won't see many people at all. We spent four days there about two years ago and loved it. There's a trip report on our website in the destinations section:
backpackthesierra.com

And there are about 75 hikes on that site—some of which will also meet your specs!

Do you mind a little cross-country navigation? If not, that REALLY opens up some opportunities for you to avoid people and see amazing things, both in Yosemite and Emigrant Wilderness…

But fairly uncrowded, would be the Grand Canyon of the Tuolumne.