The size of an ActivityPub payload overhead is minimal.
On each individual server they are ideally saved based on their unique identifier (which are RFC3987 IRIs) and I doubt that there is any software that will do it individually for each inbox instead of storing one copy to which each inbox links to.
To minimize even this, each server can store just the IRI(which is mandated to be de-referenceable) and load the payload when prompted by UI. I doubt that anyone does this also.