Is there a way to differentiate between spiral and elliptical galaxies in the TNG 50-4 data catalog?
There are no morphological measurements pre-computed in the group catalogs.
However, several post-processing catalogs would be useful for this task, or else you can compute yourself a metric of interest, based on either kinematic or photometric classification techniques. For using something which already exists, consider the Stellar Circularities catalog. There isn't much else available for TNG50-4 specifically.