You cant "add primer" in that sense.
here's the relevant definition by Oxford dictionary
primer -noun; primers- plural noun
a substance used as a preparatory coat on previously unpainted wood, metal, or canvas, especially to prevent the absorption of subsequent layers of paint or the development of rust.
a cosmetic applied to the face before another product, intended to improve the coverage and lasting effect of the second product:
"it's best to apply primer around the eye to help the makeup blend properly".
I would call it a topcoat without need of a primer. In that application it is more about adhesion, and low soak, meaning less coats on a job.
A primer is a "introduction" "a base". Sandable fillers, sealers, or barrier coat, choice are about doing it right for the job.
Those same low soak, high adhesion chemicals might be an issue on foam.
A neutral primer choice should not react, if chosen correctly. Once dry it should form a barrier that would allow a carefully applied top coat, or even other primers. After a couple careful selections, you should be able to eventually topcoat with more paint types, without a reaction.
I.e For a "Get er done" low buck room painting. I might choose it.
But a "Real rooms" paint is usually 2 coats of primer, 2-3 top coats, with sanding between each coat, and oil base or stain on the trims.