Not bubble algae. To me the picture in display tank looks like bubbles stuck in cyano. And just a lot of bubbles in what I assume is cheato.
Did your skimmer go mad and dump a bunch of bubbles into the system? Or a pump suck in air somehow? Or a baffle in your sump not trapping bubbles for some reason.
Just my thoughts could be way off though.
I recall when I had a fresh water tanks plants occasionally produced bubbles do to photosynthesis, not sure of large amounts of cheato can do the same.