> all PROCESSING branches that have synced successfully in the last 7 days
By construction, there can be none of those. Once an import job is successful, the importstatus is set to SYNCING. So, "available verified" is SYNCING or STOPPED.
In my opinion we should omit imports which are no longer updating for some reason. So STOPPED imports should be ommitted, but also SYNCING imports that have not succeeded in some time (7 days seems reasonable).
The filter could be something like "importstatus == SYNCING or datelastsynced > 7 days ago"