It might also be referring to poison gas traps
Although the example traps in the DMG doesn't include a poison gas trap, there is an example of a poison gas trap in Xanathar's Guide to Everything, under Complex Traps.
It's called a Poisoned Tempest trap on pp. 120-121. This trap has two effects, the first of which is called Poison Gas:
Poison Gas (Initiative 20). Poison gas floods the room. Each creature inside must make a DC 20 Constitution saving throw, taking 33 poison damage on a failed save, or half as much on a successful one.
It also has a second effect, called Tempest, which includes a table for various effects, two of which relate to gases (I've excluded Explosive gas and others that doesn't relate to breathing, even though most of those I do include only imply that breathing in the gas is what causes the effect):
Hallucinatory gas scrambles the mind and senses. All Intelligence and Wisdom checks made in the room have disadvantage until the Tempest element activates again.
Weakening gas fills the room. All Strength and Dexterity checks made in the room have disadvantage until the Tempest element activates again.
Poison [gas, I presume] floods the room, forcing creatures to make saving throws as for the Poison Gas element.
So, from all of the above, regarding the Poison Gas effect and that last option which works the same, you'd have advantage on the saving throw thanks for the necklace of adaptation. The other two I quoted don't involve saving throws, but a DM might reasonably rule that you aren't affected, thanks to your necklace of adaptation.
For a "real" example of such a trap, in The Forge of Fury from the Tales from the Yawning Portal, on p. 42, there's a poison gas trap:
Poison Gas Trap. A pressure plate is set into the floor about 5 feet in front of the statue. When at least 20 pounds of weight is placed on the pressure plate, it depresses into the floor, opening the statue's face to reveal a nozzle from which poison gas sprays out in a 15-foot cone. Each affected creature must succeed on a DC 12 Constitution saving throw or become poisoned until the creature finishes a short rest.
Once again, your necklace of adaptation would grant advantage on this saving throw.
However, "make it up" is likely how you are meant to handle this generally
The above traps explicitly mention poison gas, which definitely comes under "harmful gases and vapors", but beyond that, it would be up to a DM to decide what counts as a harmful gas or vapor. I do, however, agree with you that it is vague (I mean, "some dragons"? Would it have been that hard for them to enumerate them for us?).
Your suggestions of faerie dragon's Euphoria Breath and other breath attacks that relate to poison, acid or steam are reasonable, but I don't think you're going to get any clearer guidance. There any many things in 5e that require a DM's adjudication, and the 5e rules intentionally leave a lot of this open-ended for that reason.