Sizing is just a thinned-down paste.
That is a modern interpretation of sizing, in fact, the size I was taught to use way back when is amongst other things, melted horse hoofs, smells horrible and sticks the proverbial to a blanket.
If I had to paper over dry wall in the UK I'd use oil-based primer sealer, scuff sand it when dry and unibond it.
I used to "size" with Beeline primer sealer, which is a waterbased "PVA" product. It was promoted as a decorating solution, rather than "just another PVA builders' product" so it presumably had some added magic ingredient, (he says in ignorance) It isnt available any more but it did seem to work well as a "size" even on glass, laminate...