As far as I am aware, plasma activated water is simply water which has extra oxygen available for a short period. It is well known that while oxygen is essential for most types of life, in high doses it can actually be poisonous, and for this reason it can be used as a cleaner and sanitizer. Peroxide is actually produced by plants in their germination phase (Barba-Espin, G. et al., 2010. Interaction between hydrogen peroxide and plant hormones during germination and the early growth of pea seedlings. Plant Cell Environ., 33: 981-994.)
It's not really unusual for a bean to germinate after a long time, although your high reported percentage is certainly remarkable. We might imagine that immersing the bean seeds in high oxygen environment has a cleaning effect, and bean seeds have a lot of "meat" in them which lettuce does not. At normal temperatures, even in a sealed container chemical processes continue and viability declines, although Vilmorin-Andrieux "The Vegetable Garden" claims that the viability of beans and lettuce seeds are similar.
If your experiment was to be repeated scientifically there would need to be a control group of seeds not exposed to the plasma water, and perhaps another treated with peroxide the same way some fruit growers treat fungi with peroxide instead of pesticides. Comparison of the three groups would show whether plasma treated seed was an improvement over other methods.