Catalytic carbon is not normally effective for removing iron or manganese, but is beneficial to remove H2S which causes rotten egg odor.
If you are injecting hydrogen peroxide before the CC, then the carbon will be removing the peroxide before it has had opportunity to oxidize the ferrous iron from the well, to convert it to a ferric state, to allow it to be removed by sediment filtration.
Your 6.5 pH level is also working against you. Removal of iron and manganese will be most effective with a pH >7.0, so you may want to install an acid neutralizer as an initial treatment method.
For iron, manganese & H2S reduction, the usual recommended media is Katalox Light. KL is also beneficial for sediment filtration as it is capable of removing particles <3 microns.
As you mentioned IRB (iron reducing bacteria), although IRB is not harmful, if you do wish to remove it, then for the presence of any type of bacteria, peroxide would not be recommended as it increases the oxygen content which will feed bacteria and cause it to proliferate. To best neutralize any type of bacteria, chlorine or ozone is recommended. Both chlorine or ozone (O3) may be utilized directly with KL media, so chlorine will often be injected directly prior to a KL filter, or ozone maybe drawn into the KL tank, utilizing an AIO3 system.
While the KL media will remove iron, manganese, H2S and other sediment particles down to ~3 microns, your existing CC backwashing filter should be located directly following the KL filter, to remove residual chlorine and other chemical contaminants, while also polishing the water before flowing to the home's fixtures.
