I think you want [`gdal.VectorTranslate()`][1].

At it's simplest, your code turns into:

    from osgeo import gdal

    fgdb = r"C:\GIS\data\somefilegeodatabase.gdb"
    outdb = r"C:\GIS\data\testdata\OK.gpkg" #Does not need to be created in advance
    
    gdal.VectorTranslate(outdb, fgdb)

  [1]: https://gdal.org/api/python/osgeo.gdal.html#osgeo.gdal.VectorTranslate