I finally figured out where Naiomi Wildman's mother went! Temporal Investigations sent her back to 20th century Earth after some extensive plastic surgery and an education in oceanography in order to preserve the timeline.
After Picard/Discovery I don't have a good read on the Federation any more, but I kind of feel like they absolutely would have shipped her back to her own time, rather than assign her to a science vessel after what must have been like a ten minute orientation.
Well the time travel thing is extremely high risk, so sending her back wouldn't be easy, nor chosen lightly. Plus her skills as a marine biologist would be invaluable to keep the time traveling whales healthy and alive so they didn't have to go back and get more next time the probe came around.
But yeah, they did seem to just hand her a uniform and throw her at a starship, eh?
I don’t think she specified that she would be on a starship. I would guess it’s a seafaring ship, dedicated to following George and Gracie around for study and caretaking. As you say, she’s the only one left with the skills, not to mention the personal connection.
Seems to have been inducted into some kind of child rearing and adoption cult by a former disgraced Starfleet commander who was accused and seems to have admitted to sexual conduct with several minors.