...and the implication of that is that if we change the monetization model, then the metrics also change.
For a company selling a paid product, metrics become things like the effectiveness of the sales funnel, how much support the average user requires, the rating of the product on app stores, etc - which are not ideal, but still far better than "engagement".
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?
A user's engagement with your product is a great metric, because what you value is users using your product.
But for a COMMUNITY it's the wrong metric, because you don't value negative comments in your Slack no matter how many there are (in fact, the more there are the worse it is).