If anything I would count her more as a Robin 3.5 with the way things stand. Damien is the true Robin 4 in the sense that he is the 4th to have actually stuck with it longer than a week and actually served as Batman's partner/apprentice in an actual meaningful way.
Saying Stephanie is Robin is like going on one bad date that goes nowhere with someone and claiming that they were your ex. Especially when the other person in this analogy only went on that date to make another person jealous and get them back. The date technically happened but that doesn't make it a real relationship.
I don't hate your idea of going back and retroactively doing more with her time as Robin or even having her put the costume back on and having a modern run as Robin. If they did that then I would be more willing to count her.