Go to Project mode. Set the Project Filter to Active projects. Select all of the resulting projects in the sidebar, and click the Focus button. Now switch to Context mode (use View->Context Mode, *not* the Contexts perspective button that Omni puts in the default toolbar — that opens a perspective, and undoes your work here) and set the view options as you want them. Save as a perspective. You'll need to update the perspective when your list of active projects changes.
I'm of the opinion that this perspective may not really be necessary. If the projects aren't on the active list because they are stalled, or have a future start date, you're still presumably intending to do them, and those actions will be of interest. Actions from projects which are dropped or on hold don't appear in Context mode.