You can merge layers with different geometry types together with ogr2ogr.
Here is an example about merging an point shapefile and polygon shapefile into GeoPackage as a new layer "merged" that has a generic geometry type.
ogr2ogr -f gpkg merged.gpkg point.shp -nln merged -nlt geometry
ogr2ogr -f gpkg -update -append merged.gpkg polygon.shp -nln merged -nlt geometry
ogrinfo merged.gpkg merged
INFO: Open of `merged.gpkg'
using driver `GPKG' successful.
Layer name: merged
Geometry: Unknown (any)
Feature Count: 2
Extent: (309.000000, 478.000000) - (599.000000, 604.000000)
Layer SRS WKT:
FID Column = fid
Geometry Column = geom
attr: String (1.0)
attr (String) = B
POINT (382 478)
attr (String) = A
POLYGON ((309 584,599 604,466 493,309 584))
However, you will have some problems with QGIS with using that layer because QGIS can't handle points, lines, and polygons on a same layer. QGIS requires that layer is split by the geometry type
You can open the merged layer as a single layer with OpenJUMP.