An undisturbed beach at the Pine Cay resort in the Turks and Caicos in February 2026. Turks and Caicos, a chain of Caribbean islands just southeast of the Bahamas, teems with high-end, all-inclusive resorts. What many guests seemed to want, and are willing to pay thousands of dollars a night to get, is glorious silence. (Danial Adkison/The New York Times) By DANIAL ADKISON The boat skipped across the shimmering turquoise water at a breathtaking speed. “You’d better take off your hats,” the…