Wood – Removable Bracket for Wood

Sounds like trouble to me. Superglue won't do you any good, as it's only as strong as what it's gluing to (and I suspect here it would be far less strong).

Some alternatives:

• Cut away a square of drywall and replace it with the same thickness plywood, glued to whatever is behind (e.g. that metal). Then apply a thin coat of plaster, paint, and then screw into it
• Find out just what that metal is, and consider screwing into it
• If the curtains will generally hide that bracket, consider gluing a thin piece of plywood to the surface of the drywall and screwing into that

That's a common failure mode for those lamps; the threads are fairly shallow and prone to stripping out. Though if it happens immediately, rather than after a few years of use, I would definitely return it for refund and/or replacement.

If it fails after the warranty has expired:

It is possible to kluge the connection by wrapping the threat in teflon plumber's tape; enough layers will tighten the connection so the remaining threads can engage. This, too, tends to eventually fail, but you may get several more years of use out of the lamp.

Theoretically you could sweat-solder the mechanical connection, but you'd probably ruin the lamp's finish. Obviously you'd want to remove and reinstall the wiring so its insulation doesn't melt during thd attempt to solder it. And I'm not sure what solders would be compatible with the lamp's metal.

Realistically, most of us consider these lamps disposable. I just discarded one myself, after scavenging some parts that I'm planning to reuse.