Zinsser Cover Stain is a solid option. It's oil based and not moisture vapour permeable but resists the wood staining the primer, I use it on any wood that has been stripped and most new wood. Zinsser 123+ often works well enough on new hardwood as long as there are no problems with staining which varies from one piece to another in my experience.
I would normally add an undercoat matching the manufacturer of the eggshell on top of the primers I've mentioned above.
Zinsser Cover Stain is a solid option. It's oil based and not moisture vapour permeable but resists the wood staining the primer, I use it on any wood that has been stripped and most new wood. Zinsser 123+ often works well enough on new hardwood as long as there are no problems with staining which varies from one piece to another in my experience.
I would normally add an undercoat matching the manufacturer of the eggshell on top of the primers I've mentioned above.