Search for metal brackets to join 1/4" plywood boxes

The best solution at this point is to contact a local fabricator that can fabricate a piece like this since the exact thickness of the wood is needed in order to work with the bracket.

There are places online you can order a custom piece like this if you want.

You could even 3D print it out of a metal or other tough material.

That said, I don't think that upper lip is doing anything for strength. If you put metal side brackets without any lip and you glue the joints, that can't move. Is it for aesthetic reasons? If so, could you cut something like this out with shears of sheet metal?

I think your best bet will be to look for "campaign furniture" corners. A quick search turned up this for example. Though, on re-reading your question, the linked example does not have the extra lip you want, I still think this is the right terminology for the thing you are looking for.

Try corner protector for boxes. I found some similar ones using that search. I didn’t try hard enough to find those exact brackets but some came close.

A few search's led me the term "plastic stacking corners" OR "box stacking corners".

Here is one example.

There are several kinds of those but i was not able to find metal ones.

I did find a metal corner that is not what you have referenced but could work.

It seems you could also use a piece of angle aluminum fastened around the the outside corner (or inside corner) with screws, so it sits just higher then the top of the box.