My understanding, and this is totally without citation because I'm exhausted, is that hydrogen peroxide steals hydrogen molecules, which destroys fragile cell walls. That's why it fizzes. Single cell critters and plants have cell membranes that are permeable because they don't have, you know, mouths and stuff. Plants and vertebrates have stronger cell walls on external areas because their function is to keep inside stuff inside and outside stuff outside. Invertebrates tend to not have such protection. Critters with exoskeletons breathe through spiroles, so any toxin gets deep unto their insides very quickly. Critters whose bodies have to change shape quickly and easily can't do so as well with strong external protection, which is why snails, for example, go into their shells when there's a water quality issue.
There is something about gram negative and gram positive that comes into play.
When I used H2O2 on cyanobacteria, I used a little medicine syringe.
