I used to pooh-pooh the idea that a little peroxide could release a useful amount of oxygen, but then I read the same claim from multiple people I respected. I think that is part of it. Sometimes soil is so hypoxic that even a little soluble oxygen, released right where it is needed, helps roots or encourages "good bacteria" or discourages "bad bacteria".
I think there is also a direct disinfecting effect. Hydrogen peroxide does kill some bacteria and fungi. That probably helps deter seed rotting and stem wilt / fungus / damping off.
MAYBE it also deactivates SOME kinds of germination inhibitors (helps break dormancy).
I hope you post info from sources you find! I have a lurking suspicion that gardeners have preserved and passed on wisdom, lore, myths and fallacies going back to Neolithic agriculture. At what point do we wean out the untrue beliefs, if everyone follows them and repeats them?