Edit: hmmm, I can't find an exact match... And it lacks holes where it would need them, but almost looks as if it had been spot-welded to something, like perhaps part of a toy like you were thinking. I think I've seen wheels on a toy attached to an axle this way. Hmm... Uncertain
Some buckets have things like this on it for the handle to hook into.
But the hole is square so I was thinking a tool with a square steel shaft going through this and a wooden handle maybe.
As far as the shade bracket I think this is steel and don't think a nail will go through it.
Thanks nhbenz for mentioning the spot weld . I know the hole looks square and I think it was for a bucket.
I found an old bucket all rusted away and these look close so I'll mark it solved .