Some MapBasic tools (such as Coordinate Extractor) create new columns in open MapInfo Native (TAB) tables. You cannot alter the table structure of open GeoPackage tables in MapInfo Pro, so you cannot create new columns on these tables. Make sure any columns you need to update are in the table before working with it in MapInfo Pro.
There are tools available to alter the structures of GeoPackage tables outside of MapInfo Pro, such as www.sqliteexpert.com). If you alter the structure of a GeoPackage table, then you must reopen the GeoPackage file (*.gpkg) in MapInfo Pro to re-generate a new MapInfo table that is aware of the new table structure.
Warning: Use a tool to alter a GeoPackage table at your own risk.