EAST HAMPTON, N.Y. — Beyond a thicket of dahlias, Katie Couric climbed through a tangle of vines to pick a squat little eggplant. Each week during the summer in this beach hamlet, she takes inventory of her vegetable garden, and on a mid-September Saturday, the patch of soil was bursting with shishitos, jalapeños, and cherry tomatoes.

She should have brought a basket, she decided, holding an armful of veggies. “Some of them are breaking, but they’re so good, they taste like candy,” she said, before rubbing a yellow tomato on her pants and popping it into her mouth.

Ms. Couric, 62, often broadcasts her harvests on the “Story” section of her Instagram feed, where, like many public figures, she invites followers into her world. Having invited NBC viewers into the exam room for her colonoscopy in 2000, Ms. Couric is arguably a pioneer of oversharing, but back then, she was less open to sharing details from her personal life. (Her first husband, Jay Monahan, had died of cancer two years before.)

On Instagram, Ms. Couric embodies the “Today” show version of herself: the fun-loving mom who can pivot from hard news to “pajamagrams” and family photos. The trick is keeping her 715,000 followers involved. When news of the impeachment inquiry broke, for example, Ms. Couric asked her followers, somewhat un-Instagrammishly, what they thought about it.