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Does the Kappic Eagles Detachment ability work on Aerial Drop. Might sound incredibly weird, but here's the wording from Aerial Drop.

During deployment, you can set up this model in a high-altitude transport, ready to deploy via grav-chute, instead of placing it on the battlefield. At the end of any of your Movement phases the model can make an aerial drop – set it up anywhere on the battlefield that is more than 9" away from any enemy models.

So Aerial Drop outlines that they are embarked in a high-altitude transport, and the turn you deploy them they have disembarked the transport to make a grav-chute deployment.

Am I overthinking it?

You're overthinking it.

It also doesn't say they've disembarked
Mostly because you'd struggle to measure 3" from the hull of the vehicle that doesn't exist