The feed can be filtered by badge, eg
https://www.wikitree.com/index.php?title=Special:NetworkFeed&badge=pgm
shows you all recent activity by PGM members. That includes work outside the project area. But you could use it to find project members who aren't doing anything at all.
Or, you can check to see who appears in the feed for the Project Account's Watchlist, e.g.
https://www.wikitree.com/index.php?title=Special:NetworkFeed&who=WikiTree-30&watchlist=1
shows activity on PGM Watched profiles, including meddling by non-members.
For some small projects, that will do it, because they aim to Watch all the profiles in their scope. But it doesn't scale up. Other projects have a scope that runs to hundreds of thousands of profiles, maybe millions. They can't have them all on a Watchlist.
But presumably any work anywhere in that lot will qualify a member to keep the badge.
And you can't put a project tag on a person-profile, and you can't get a feed for a category. And in any case, it would be impossible for the big projects to mark up all the profiles in their scope.
For some projects, you could try to guess the project by looking at places and dates. This is already done for some DD reports. If it works well enough, it could be applied to the badge feeds. Then you'd have a feed of project-related activity by project members.
But you could also do project-guessing on the global feed. Then you'd have a feed of all project-related activity by all contributors, not just project members. This would probably make the project members list look a bit silly, and weeding it out would look a bit pointless.