Giger has done only a few doodles on napkins based on the Spaith script.
You can see them on the bluray.
But that moment when you see himin the art dept is just a visit, he never worked there, nor really on the movie. When Scott and co were still not sure if it was or not an ALIEN prequel (wich was undicided until the very end of the shoot, just listen to some of the artist involved in the making of Furious Gods) they tought it would be good to have him involved at least for publicity, to apease the fanboys.
The chair is based on Gigers original design but was reworked/finalized by Ben Procter.
They used some parts of his facehugger cycle of life paint on the Engineers headroom ceilling.
Giger is not anymore the artist he used to be, Scott wanted to work with himbut saw he was not anymore up to the task, he also wanted to be able to use the harkonnen castle as the Engineers base so he got him on the payroll to ease the process.
Giger and Scott are not friends.
From day one it was clear that Fox executives would not let giger design stuff, why because it was considered way too sexual and morbid yeah quite crazy huh?
But it already happened with ALIEN, but at that time execs were not so present on set and all and basically Scott kept everything under wrap untilhe almost finished shooting, when it was too late to go back.
Here the design are inspired by Giger's work but they are tamed, mechanized.
No more sexual, no more scary but scifi.
Well it still works
But yeah Giger has sadly almost no real input in the movie, the thing is that Scott at first tough the could do without the giger esthetic, look at the designs for the temple in the artbook, he wanted to do something really completely different but its the artists who pushed him toward that and finally realizing that he was going to come up with stuff has scary as Giger's that he decided to go back.
But evene when he did that he managed to screw it up a bit by not using the great stuff Carlos Huante did wich was and is beautifully scary, twisted and a perfect follow up to Giger's work on ALIEN.