QGIS to ArcMap file delivery via geopackage

ArcMap should be able to open a GPKG, but you may need to follow these steps (I don't believe you can drag and drop)

Alternatively, you can export to ESRI SHP direct from QGIS, although bear in mind this has limitations on field name length (processing tools default to GPKG, but right click on a layer -> Export -> Save As/Save Features As and you should have many more formats)

Shapefile has so many limitations, it's hard to imagine that this would be the preferred exchange format (I'd prefer UTF-8 CSV with Well-Known Text geometry over shapefile). In any case, the .sbn/.sbx components are not part of the shapefile specification, and therefore should not be expected.

It seems the limitation is on the user's part more than on the software, though if this person's Desktop release is elderly (<10.4) there could be geopackage compatibility issues.

QGIS should also be able to create file geodatabase (with the Esri, not Open, FGDB library).

You should be able to negotiate an acceptable format with a little flexibility on both sides.

I guess they need the files in shapefile format instead of geopackage. Whatever is the file you have to exchange with them you could just export it as shapefile from QGIS. You can do so by right clicking on the file in QGIS, clicking export objects as.., the selecting ESRI shapefile on format and then saving it within the folder directory you want. Aditionally you could create a zip file with all the files that you just produced to make file exchanges easier.

If you have the GDAL/OGR command line tools installed you can convert a geopackage to a folder of shapefiles (and .dbf files for non-spatial tables) in one line. I'm not sure how to get these installed in Windows/Mac (am using Linux) but it is possible.

I have a geopackage with two layers:

$ ogrinfo -so -al data.gpkg | grep "Layer name"
Layer name: localauth
Layer name: inhours

and if I do:

$ ogr2ogr -f "ESRI Shapefile" shapes data.gpkg 

I get a new folder called "shapes" with:

$ ls shapes
inhours.dbf  localauth.dbf  localauth.prj  localauth.shp  localauth.shx

which is one non-spatial layer (inhours.dbf) and localauth shapefile set. If there were more layers they would appear here.

I could now zip this folder up to send to someone who really really really can't deal with a geopackage.