Do you think the logger would easily be able to log instead to the localStorage rather than the console?
Perhaps then the viewer portion could have a listener to localStorage changes and refreshing it’s store?
This way a second debug browser tab would be able to persist the log across page loads.
Perhaps a controller object could watch and prune the localStorage to ‘occurrence’ and ‘duration’ limit settings per category?

Is this close to where your headed with the code?
Does is sound viable?