We had to update our FMOD integration to 1.10.13.
I deleted the old FMODStudio plugin from the project and replaced it with the new one.
Deleted the FMOD folder from the Content library and rebuilt the whole project again.
Nothing else has changed otherwise.
In editor everything is fine, not getting any plugin related errors or warnings.
However there are no FMOD sounds in the packaged version, only inbuilt unreal sounds.
No idea where to go from here.