You might be surprised to discover that even for paid products, engagement is often still the #1 metric.

Simply because people who are engaged with a product/app/whatever are by far the most likely to be repeat customers -- to renew their subscription, to buy the new version, to adopt the next product.

Once engagement drops, future revenue dries up. A drop in engagement is the canary in the coal mine -- it shows where your business is going wrong months/years before it shows up in sales stats or renewal rates.

So actually, the metric doesn't change at all. E.g. Netflix is obsessed with engagement even though it's subscription-based rather than ad-based. Because guess who winds up cancelling their subscriptions?