Technically, we have no idea WHAT rank the Janeway hologram holds, if any. She may appear with pips, but Starfleet (even in the Prime timeline) was reluctant to acknowledge the Doctor's rights, and we're only 5-6 years on. I doubt they've allowed holo-Captains in the interim, especially in the more... reactionary... Kelvin timeline.
The Prodigy interviews thus far have said that its
Captain Janeway as a hologram.
Also, Voyager crew made the EMH the ECH in case of emergencies and it was a success. I don't think Starfleet would shy away from allowing Captain Janeway hologram (who already has command experience and is based on the real Janeway) to take charge if its really needed in the same manner the ECH did.
Correct me if I'm wrong, but it wasn't Starfleet which was reluctant to acknowledge the Doc's rights, it was the judge.
If anything, Starfleet (aka his Voyager crew) and Barclay in the AQ who advocated for him, backed him up... and while he may not have been recognized as a person by the judge at the time, he was given the ability to control his work.
5-6 years is a long time... and I doubt some more progress wasn't made in that regard (at least as far as the Doctor goes).
Also, the judge's decision likely wouldn't have had much of an impact on Starfleet itself. So if SF wants to grant a holo captain to take charge if its necessary... then it will be able to.
Also, STO is not canon, so there is no reason to use an example from there.
What does Kelvin timeline have to do with being more 'reactionary'? How is it more reactionary? Genuinely asking as I'm a bit confused with the wording here.
Thus far, we've only seen a small portion of the 23rd century in that timeline... not the 24th. Holograms like the doctor weren't exactly common place in the 23rd century... so a lot could have changed in 100 years on AI front and SF's stance on using holograms for assisting the crew or taking over even in case of emergencies.
I believe the original statements about Prodigy (once it was revealed Janeway would be present) were that the hologram is intended as a training/advisory tool for lost Starfleet crews. So likely not programmed to act exactly as the "take charge" original would.
Yes, it was stated she's a training hologram... but (again) with a rank of 'captain'.
However, I don't see why she couldn't take charge of the Protostar like the ECH took command of Voyager.
Janeway holo is based on her after all, and as such would likely been programmed with command experience... especially if a ship is full of teens who have limited or no idea of how a real starship works - although SF ships are really easy to use through verbal computer interfaces.
The rank is odd to me as I would have thought the hologram of Janeway would have used her latest rank.