Proper code below:
from osgeo import gdal
gpkg = gdal.OpenEx('path_to_gpk',gdal.OF_OF_UPDATE,allowed_drivers=['GPKG'])
error = gpkg.DeleteLayer(0)
# this code is also possible as an alternative
# doesn't seem to delete everything though, so possibly DeleteLayer() is better
# gpkg.ExecuteSQL('DROP TABLE [layer name]')
The answer seems to be that this cannot be done, at least using the current versions of both packages. Because as, you noted, the latest versions of fiona and rasterio rely on different GDAL versions. There is likely an older version of rasterio (1.0.*) that could use GDAL 2.4.1.
I have been using fiona (1.8.6), rasterio (1.0.22) and gdal (2.4.0) fine in ...
It is an new feature in the future release QGIS 3.10. QGIS can now read ESRI TIN as this format is now supported by the MDAL library.
Finally, it seems it will available in the future release QGIS 3.12 (end of February 2020).