Not sure what you are trying to do here. You want to tint the whole paper magenta and then print cyanotype over it or you want to tone cyanotype with it. If latter, it is good that it does not touch the paper. That way your highlights will stay white. You might want to try and see what happens when a printed cyanotype is treated with tit.
I had understood that the Declaration was written in pokeberry ink because there was a shortage of the desirable oak gall type -- but maybe I heard/read wrong. Oak gall is so permanent that it's responsible for the whole concept of a palimpsest -- a document that's been erased (scraped, on parchment or vellum) and overwritten but the original writing is still readable with care -- so fading of that ink wouldn't be a major concern for conservation of the original Declaration.
Either way, I can't think of anything other than sizing that would make watercolor paper impervious to pokeberry ink. Maybe there's more to making the ink from pokeberries than just boiling the juice?
In order for poke berries to be most useful for alternative processes, you have to get it to bind selectively to either image or non-image areas.
The experiment that left paper untouched is actually a good sign. The beautiful dyed yarn is another.
Don’t actually know how to make image or non image area attract dye though. There is oil and water in lithography, batik
/ waxed fabric and those dyed Easter eggs.
The chemists here might know what things can bind to Prussian blue, and then what things can bind to poke berry juice