Can the OGC GeoPackage Writer write metadata?

I don't think the OGC Geopackage writer can write metadata. You can however use the SQLite Non-Spatial writer to write metadata, since a gpkg is an SQLite database. Check out this documentation on gpkg metadata: https://www.geopackage.org/guidance/extensions/metadata.html#gpkg_metadata

Looking at that document, the entire metadata document is a single value in one row of a table!

I suppose that this is also how metadata is stored in a fileGDB? I don’t know the internals of fileGDB, but FME grabs the metadata as geodb_metadata_string, which is extremely long

geodb_metadata_string is an XML representation of the metadata of your FGDB. This goes in the ‘metadata’ column, you can specify XML in the ‘mime_type’ column.