A foundry is for melting metals, so you can pour them into molds- casting.
A forge is for heating metals so you can bend, twist, cut, or otherwise shape them- forging.
It definitely looks like you've got a forge there rather than a foundry. And if there's an anvil stand, that would be confirmation.
Now, I'm not pointing this out to pick on your terminology. It's good to know which one is which is which so you can search the right places and find what you're after. I haven't seen anybody rework a brick forge to run off a rocket-style
wood burner, but I haven't searched for it either. I DO do some forging, and I'd be surprised if you were able to do it well without air control. You don't normally work with your fire constantly running at max. If you're hoping to forge some steel, then you'd google things like, 'brick forge', 'rocket forge', 'rework old brick forge', 'add rocket to old brick forge', 'install rocket to existing forge chimney', etc.
On the other hand, if your "metallurgical purposes" are casting rather than forging, that might be another story. You'd want an insulated container for your crucible to sit in, where the rocket output would wash across it and heat it up. Those, you DO just run at max until your pour is ready (that is, until whatever you're melting is all liquid and ready to go). I don't see a convenient way to build such a container with the forge setup in the picture there, but that doesn't mean it impossible. If casting metal is what you're hoping to do, then you'd google things like 'wood fired foundry', 'rocket metal foundry', 'rocket metalcasting', 'build rocket to smelt aluminum', 'add crucible furnace to existing chimney', etc.
I hope that helps!