I don’t recall exactly where I heard this, but someone was reviewing a videotape of the baptism (which I’m guessing was done sometime and the 90’s), and saw/heard that the priest did the “we” form instead of “I”. This person brought this tape to her priest, who after viewing conditionally baptized her. Or at least that’s how I remember it.
Regarding baptisms in general, and especially those done outside the Church, I have found this to be a decent guide: https://www.dosp.org/wp-content/uploads/9_3.-Valid-and-Invalid-Baptisms.pdf