I'm currently trying to set up Gadgetbridge (https://gadgetbridge.org/) on Graphene OS.
The app requires permission to display over other apps, and takes me to the corresponding setting.
But for some reason I cannot enable the setting. I always get a big popup saying

"App was denied access
Access to this permission can put your personal...."

And there is only a OK button. No way to enable this.
How can I grant the app this permission?

if you open the app info (either by long pressing on the app icon in the launcher or getting to the app info through Settings - > Apps), do you possibly have a 3-dot menu in the upper right corner? There might be a toggle to allow restricted settings.
Btw, just installed Gadgetbridge myself and had no trouble giving it any permission, so check if your app is up to date.

Seconded, you have to enable access to restricted settings via the app's system settings page, then the three dots in the top right.