That simply looks like a mold growing on the medium, and is likely unrelated to the spots on the plant.
My recommendation is as follows:
No hydrogen peroxide. It is entirely too energetic in its energy release and can damage tiny root hairs.
Physan can be effective, but over the years I have moved away from disinfectants because they are indiscriminate, and now highly recommend living microbes sold as plant probiotics - analogous to using beneficial insects to kill bad ones.
I have found Inocucor Garden Solution and Quantum-Total to both be effective. Q-T is also sold as the privately-labeled “Quantum Orchid” at a higher price.
The microbes within them predate pathogens, secrete antibiotics to prevent future infections, and have various other beneficial properties, including growth stimulation. I have used both over the last 7-8 years, have seen essentially no rots of diseases in my orchids, tropical plants, flowers, shrubs and trees, herbs vegetables and fruit (a fig).
Here are a couple of things to read about them:
What do plant probiotics do
Comparing plant probiotics