I think I had the same Algae in my tank last year or 2, I purchased some stuff to treat cyanobacteria but it didn’t work as expected (at all), like what you said, you touch it and it breaks down, and is very easy to move most of it away.
Although I can’t fully remember what I done at the time to correct the problem, other than a couple of extra water changes and siphoning the water from the affected areas, it eventually went away on its own and to date hasn’t returned.
Sorry I know this probably isn’t much help but hopefully a couple of extra water changes can clear it up for you.
All the best.