Note that the body and the cap seem standard across their set, but the tangs seem to differ considerably. Or are they all the same length but happened to be inserted loosely to different depths in the body?
The existence of the cross-pin suggests the depth of the tang into the body is intended to be constant even if the hole depths are not very repeatable- though why they should not be, I cannot say.
You say above that the pin is “solid” on some of these. That could simply be by rust. The pin seems to have done more than simply hold the spike in place- unless the extra length is to allow its ready removal when dismantling The Thing in its normal use. In which case one might expect it to have a neat little knob or at least a screwdriver slot.
Try considering what we might drive the tang into. Unless something like a lawn, it would need be reasonably substantial or well re-inforced to avoid being riven apart.
They don’t seem strong enough to be handles for carrying hefty loads, and coffins were probably always fitted with their own handles.
What though, of being anchors for something like cloth screens, curtains or nets, with the tang driven to a predetermined depth into a soft plug in a hole in the wall? The fabric fitted with large loops, rings or hooks; the pin stopping said loop, ring or hook going too far back along the body? Just a wild idea!
Can we work out what the cap does? What is its shape on the hidden side?
The little notch in the rim of the cap standing on its own: does that look deliberate, as if to clear something, or accidental damage?
Might these be some sort of temporary legs for something perhaps dismantled for transporting or storing?