First, avoid the superlative. As you point out, focusing on THE most popular story nets a beige wash of gray, a productivity wish, a set of boring platitudes that kinda appeal to a kinda lot of people.
Instead, encourage some darker, bolder hues — find a band of related topics and tie them together. Encourage the unmarked moderators, the ones who find three things to link to because they have something interesting in common — or contrast.
Police these corners so they don’t become toxic. This isn’t Reddit.
Second, find compelling authors and engage with them directly: hire them to do what they’re already doing, but more and more visibly. They are your content creators: they make your product successful. Reward them richly.
Third, help readers realize what brands/authors they like. Right now the Medium brand is too strong, and washes away individuality. Find a balance shifted more towards a thousand community vegetable gardens, rather than one big bland potato.