Reaction of H2o2 on Ozone in jar washing Tank in packaged drinking Water Company
Both ozone and H2O2 are reactive oxygen species. They don't necessarely react with each other, but oxidize organics and act as bacteriocides. Majority of bacteria are killed by H2O2 (which is cheaper and safer). In case some spots were not cleaned ozone is added. Producing enough ozone to clean it all would be difficult. Guaranteeing that H2O2 reached every spot is also hard. this is why they use two chemicals.

0.5ppm (1/2 parts per million) is a relatively low dose, but working with ozone at higher concentrations is dangerous. Ozone is more toxic than chlorine.

So, this is much like mixing dishwashing liquid with laundry detergent. There is no reaction between them.

Note that in a lab you can have O3+H2O2 -> H2O3 + H2O, but you have to run it at low temperature, the yield is low and the product decomposes fast.