I think making the person to protect NotJohn in this movie a ManMachine hybrid could be interesting, but they don't seem to have taken advantage of it in any way.
The original Ghost in the Shell is all about an AI becoming self-aware and asks the question, how and when a machine can become equal to a human/living organism.
The sequel goes the other way around, where people's conciousness is put into robot bodies and here, the movie shines a light on the question "When does a human become equal to a machine?"
I think that could have become an interesting aspect to explore in this movie... and watching an augmented human being go toe to toe with a Terminator should be awesome, but somehow, it seemingly isn't.
But John didnt really make a choice
He wanted to save his mom because he wanted to save his mom. While the T-800 advised him it wasnt tactically sound there wasnt any motivation for John to have to decide with. There was never a chance he was going to NOT save her
Frankly, this whole argument sounds sort of like a very nitpicky rundown of every moment John showed agency and trying to come up with weird rules on why that doesn't count.
That point about him saving his mom highlights that issue.
Is John a strong protagonist with lots of agency and acitvely shaping the plot? No.
But he's not just some McGuffin Winning Condition as that one soy-post earlier implied. He does show agency, he does interact in ways with other characters to influence them actively. He has to react to a lot of shit, but to go off on a bit of a weird tangent:
In Titanic, Rose and Jack react to the Titanic sinking, that doesn't make them McGuffins and it doesn't make the iceberg or the ship the protagonist. That is to say: A strong protagonist is someone who acitvely shapes the storyline, but depending on the plot, a protagonist can be forced into reacting to the outer circumstances, ie: John who has to react to his mom setting out to kill that black scientist dude. He also orders Arnie not to kill anyone early on,
which affects the plot throughout the entire movie. I guess one could argue that John's arc in T2 is to transform from being a passive person that has stuff happen to them to someone who makes some decisions and shape their own fate, even if it's only a small start. If you go for that argument, you could also claim that T2 thus shows how the very events of that movie shape him to be a bit closer to the kind of person that he needs to be to defeat Skynet in the future.
But I digress, the point is that John, whether he's an active protagonist or not, still is a character, not just some tagalong plot device.
That John chooses to risk himself for Sarah is part of an ongoing theme in T1 and T2 about the importance of family, and more specifically is about John's compassion and willingness to sacrifice his own life and happiness for others.
The movie doesn't beat you over the head with it, but the question does arise:
If mere survival is the goal and we sacrifice our ideals, our loved ones in the process, what point is there in survival?
That's why John's decision to rescue his mother/prevent her from killing Dyson is so important.
Future John Connor has to be the kind of guy that is willing to sacrifice everything to rescue others, otherwise he won't be the leader that rescues humanity.
By deciding to rescue his mother, he becomes the person that can safe humanity.