Arrange tomatoes, peaches, and plums on a large rimmed plate or platter. Sprinkle with sea salt.
Strain shallot and chili from the lime juice and scatter over the fruit. Tuck burrata throughout.
In a small bowl or jar, measure 2 tablespoons of the reserved lime juice. Whisk in 3 tablespoons olive oil. Drizzle liberally over the salad, tossing just slightly to make sure everything gets a kiss of dressing. Top with fresh herbs and several twists of pepper. Add sea salt to taste. Serve immediately.