[Heel n Toe]

Unless you're just really into the industrial look (trust me, it's a thing), you'd probably be happier long term if you got it primed it with something that would suppress any kind of corrosion and then finish with flat or eggshell white the same color as the ceiling.

How much footage of this ducting do you have in the entire place? If you decide on priming and painting all of it, is that a big ask?

If you do go that route, tell them you want to see each application after it's done. You don't want them to cheap out on you and just paint it.

The wall behind the first two pics doesn't look like the wall in the third. Was that a pic you found online, or did you take it there?