I had success with QGIS 3.0.1 this way:

• Open a layer from .gpkg databast
• Select some features
• Edit - Copy Features
• Edit - Paster Features as.. New Vector Layer

The new layer is created into the existing GeoPackage

I had success with QGIS 3.0.1 this way:

• Open a layer from .gpkg database
• Select some features
• Edit - Copy Features
• Edit - Paste Features as.. New Vector Layer

Use an existing .gpkg as a target file but give a new name for the target layer

The new layer is created into the existing GeoPackage