Harrowhark fully intended to go back to her body and consume Gideon's soul at the end of HtN.
I think the first time through, the ending reads otherwise, especially after what Dulcinea tells Harrow about something— potentially Gideon— controlling her body. But paying attention to some key details in that final section very clearly tells us otherwise:
I do think that she genuinely considered staying in the River as the Canaan house bubble collapsed, but instead she says no. She declares to herself that she's going to leave, as if almost to give herself the strength to do so.
She's already considered the options she has if she wants to avoid destroying Gideon's soul. None of them even slightly guarantee that she won't just end up back in her own body and destroy Gideon's soul anyway, because of the fact that a soul is naturally drawn to it's own body.
So, in spite of what Dulcinea tells her, she chooses to go back to her body because there are genuinely no other options left to her; it's either go back to her own body, or potentially go mad in the River and end up back in her body anyways. From what she knows, there is nothing else for her body to inhabit. There are no other known options but the two presented to her by Abigail.
That's why I think that if it was genuinely Harrowhark's intention to stay in the River and give her body up to Gideon, the narration at the end of HtN would've been very different.
It'd be weird if the narration didn't fully and clearly acknowledge— with all the repercussions that come with the choice— that yes, she was choosing to subject herself to the madness of the River to give Gideon's soul a chance.
So she chooses to go back, but when she leaves the Canaan house bubble, what happens next isn't something she expects. She's not buoyed up and out of the River and returned to her body.
Instead, she ends up pulled somewhere else:
She ends up pulled to the Locked Tomb. Or rather, some River dream bubble version of the Locked Tomb. There is a very obvious detail to show that this is not the real, physical tomb.
The altar is empty. Alecto's body is missing, even though we know for certain that her body should still be there.
So we know this is another dream bubble or something like one. But why doesn't Harrow awaken in her own body, if that's where she actually intended to go?
Because someone else is already in it:
Harrowhark couldn't wake up in her own body because Alecto had already taken her place.
We know this both because Gideon literally sees Alecto and knows she's come to take control of Harrow's body, but we also know this because Alecto's body is absent from the Locked Tomb bubble.
The chains being snapped and broken in the dream bubble represents the fact that Alecto's soul has escaped its prison, even though her physical body still lies in the real version of the Locked Tomb on the Ninth.
Importantly, her body is taken over by a soul much larger and much more powerful than hers, so Harrow can't necessarily force it out even if she wanted to. So with Harrow's body already occupied, Harrow's soul follows the only other link it could, which is the link that she's already established with Alecto's soul. That's how she ends up in the Tomb bubble.
But it is important to make it clear that Harrowhark's soul is still attached to her own body and she's not completely unmoored in the River. The final paragraph of the chapter hints to this:
While we don't know the specifics of the fight or how it even happened in the first place, we do know that Blood of Eden fights the Nine Houses. This is when they lose Gideon's body, and come into possession of Harrowhark's.
The side-to-side rocking like an explosion is mimicking what her body is experiencing in the physical world during the fight, and "faraway in a land she had never traveled" is meant to represent how her body is now on New Rho.
I'm convinced that what's going on between Harrow and Alecto in NtN is similar to what's happening with Palamedes and Camilla.
Harrowhark's body is still hers, and she's still there in some manner. But she's being superseded by Alecto, and for some reason unknown to even her, she's content to let it happen:
Personally, this course of events is a lot more interesting than Harrow purposely deciding to stay in the River.
In fact, the survival of Gideon's soul is only really possible because of some unpredictable quantity that no one was aware of— Alecto.
Alecto taking control of Harrow's body and giving Harrow's soul something else to inhabit in the meantime is quite literally the third option that Harrow was desperately trying to look for, and maybe that's why Harrow subconsciously decides to let Alecto stay in control and instead she goes to sleep in the Tomb!
It's just a more interesting read that more readily incorporates all the details the text provides us with. It paints a clearer picture of what's happening at the end of Harrow the Ninth, rather than just saying "Harrowhark chose to abandon her body for Gideon and remain in the river. Somehow, in the process of doing this she ends up in the Locked Tomb completely by accident."
My final read of it is that Harrowhark really did intend to go back. But as a consequence of Alecto's interference (whose interference was possibly to keep Harrow alive), she was given another chance to save Gideon's soul.
