I expect, further conversion to weak molecules and not complete degradation.

I am not sure you can completely degrade the dye, but you can certainly oxidise it to lower energy levels.

One alternative for carrying out this process more effectively at ambient conditions would be adding transition metal salts, like Iron or Copper salts, to the solution, thus inducing the occurrence of the Fenton reaction cycle, which would promote the generation of oxygen radicals with a higher reduction potential than hydrogen peroxide and oxidise the dye to a greater extent.

Best regards.

Using H2O2 and Fenton-type catalyst with UV, you can regenerate OH° like AOP process. By this way, I think OH° could oxidise your dye even at room temperature.

BR,