Commercial Rights for Generative Fill in Photoshop?

Apologies I have tried to find a definitive answer but struggling.

My question is; let's say I take a photo of a fence, and I use photoshop to include a bird sat on it.  Can I use this new image (created with real and AI), for promotional purposes - a shop flyer for example - or is the AI generated part copyrighted to Adobe or other?

btw - I'm certainly never going to claim the bird was real/in the photo!!  I'm just trying to get my head around the legality of all this new technology.

Hope this all makes some kind of sense.