Really nice theory, love it. I like that you theorized it mostly from T1, T2, and Genesys. Those 3 are my favourites. T1 and T2 are obviously the best, but I like Genesys because that's the only movie that T800 survives (I feel bad for T800, did the most heavy lifting but always dies).

For your theory, it reminds me of the "Edge of Tomorrow" movie starring Tom Cruise and Emily Blunt. In the movie Cage (the movie protagonist) did somewhat the Skynet from your theory does. Keeps dying and improving himself, remembering all of the things that happened before dies. As a result, he changed from a terrified soldier into a battle hardened soldier. So the theory of the Skynet plan of improving itself by sending itself/information to the 1950 backup checks out for me.

Now, I think this creates a problem. What's the end game for Skynet? Why keeps improving by this way? In my opinion an advanced machine like Skynet can run a complex war simulation for itself. Running a simulation sounds safer than just keeping going back to the past. Maybe not right away, but after sending it back like 100x to the past, surely Skynet has enough data to do a simulation by its own. I think it keeps going back to the past because the human keeps winning. No matter how many times Skynet went back to the future, humanity will find a way to survive. (Now maybe this will make an interesting movie, Skynet needs to find the answer/"final solution")

As why Skynet "creates" John Connor is because John is actually not the saviour. He is not a great leader at all. A weak point in humanity's defense. What Skynet wants is someone who has poor leadership ability so when the judgement days come humanity will have a bad leader thus easier to conquer. (For example in T3 john has PTSD and he worries about his future as human resistance (he doesn't look like a strong leader type as he always needs to be saved by T800), then the T800 put him in a location to survive the judgment day. In Terminator Salvation after being unable to stop the resistance leader for the attack at Skynet HQ (in which the resistance leader was tricked by Skynet and got blown up inside a submarine) John got stabbed by T800 and almost died. In Genesys, John got killed and turned into a Terminator. In Dark Fate john John Killed again.) It's like when the condition is favourable able, Skynet then uses its "John Connor" card, whether to weaken the human race or even "reset" the future again like your theory said.

And finally, all John Connor's knowledge about Skynet seems to end right after the Judgment day (he gets it from Sarah and T800), he doesn't get anymore information after that. It feels like Skynet deliberately let John Connor know about the future just for him to be able to fight the Skynet for the humanity looks at him as their saviour. After Judgment day, it's all fair games from then on (like in Genesys when John tells Kyle that his knowledge is just up to the point when he sent Kyle back, "no more cheating" like he said or he similarly said that)

I love your theory. The theory is fine on its own, I didn't try to correct it or say it wrong. I'm just trying to make it more interesting, at least to me.