Etihad Regional's website says nothing about having lounge access.

I'm not sure that you would even be able to actually physically access the part of the airport where the lounge used by Eithad would be located. Your journey is within Schengen; Etihad's flights are all to outside of Schengen, so I presume that their lounge may be in a part of the airport that you would not have access to with your boarding pass.

It's been a while since I passed through ZRH so I don't recall how the separation between Schengen and non-Schengen gates operates there. If you can get to the lounge used by Eithad, then do try, making sure you have your EY Guest card. And please report back with your experiences.

Edit: Etihad uses the Swissport Panorama Lounge, which is located in the E gate area. Are Schengen passengers able to take the Skymetro to these remote gates?