Personal Response
I feel like this movie is a lot more complex than I realized while I was watching it. The way I would describe it is that it is the most "in space movie" that is actually unrelated to space. Yes, the story takes place in space, but none of what truly matters is about space at all. If you do not pay attention, you might think it is just a space adventure, but it is not. And I think Cuarón did a brilliant, brilliant job with that.
What happened with Dr. Ryan? I think she recovered her willingness to live. Her conversation with Kowalski reminded her of the obvious, get out of there, survive. She realized that making it back to Earth would basically be a miracle, and that her life was worth something. Through resilience, she confronted her deepest pains and decided to fight for her life. Her turning point came when Kowalski made her realize that all the "impossible" barriers she kept mentioning were just excuses.
Some movie critics claim that she actually died, but I am not so sure about that. I guess you could interpret it either way. Personally, I like to believe she survived, that she overcame her trauma and returned to Earth successfully. And even then, Earth does not exactly welcome her back nicely. It almost feels like she was reborn. And what is birth? Horrible. You are warm and safe inside the womb, and suddenly you are pushed into a loud and hostile world where you must survive on your own. That is exactly what Dr. Ryan goes through when she lands, it is messy and painful and transformative.
I think Dr. Stone stepped out of her cold engineer mode when she realized that Aninkak was on Earth and could not help her at all. That moment humanized her. The simple act of having a fragile human connection made her compassionate. It was unclear whether he understood her, probably not, but Ryan still felt close to him. It broke my heart when she asked him for a prayer. It reminds us that in our worst moments, all we need is a tiny support system. We need to feel that somebody cares about us, even if it is a stranger.
The purpose of that part of the film was to show the other side of isolation. Here I am talking about Aninkak. In his own way, he was also isolated, just with two other people and the dogs. Dr. Stone does not know if she will die right there, but she knows the dog will. She does not know it directly, but someone else, somewhere else, is going to die regardless. The film ties their loneliness together in a haunting but beautiful way.