The wording of "Stunned" seems inconclusive to me. Does it ignore incapacitation immunity? If not, do other effects apply? Specific situation: what happens if I successfully hit an Air Elemental with monk stunning strike?
In your specific case with an air elemental:
MM, Page 124
Condition Immunities exhaustion, grappled, paralyzed, petrified, poisoned, prone, restrained, unconscious
There is no condition immunity for Stunned or Incapacitated so an Air Elemental would suffer from all of the Stunned conditions (included incapacitated).
I tried to search the MM and could not find any Monster that had the condition immunity to Incapacitated.
A stunned creature is incapacitated (see the condition), can't move, and can speak only falteringly.
The creature automatically fails Strength and Dexterity saving throws.
Attack rolls against the creature have advantage.
Stunned includes Incapacitated, but RAW doesn't say it ignores Incapacitated immunity (so it doesn't), and Incapacitated immunity doesn't mean Stunned immunity (so other effects apply).
Perhaps if you gave more information on your specific case it would be easier to understand why you are in doubt.