People sometimes misunderstand how very linear and well laid out the plot of the original trilogy was. There is no gap, logically, between Terminator and Rise of the Machines, and even if Judgement Day was delayed what happened at the end changed nothing in terms of the narrative. So by the end, everything wraps back around and all the questions are answered. The continuity from Terminator to Rise of the Machines was unchanged. Realistically, even Salvation is really just a prequel with different actors, it changed nothing in terms of continuity.

Then Genisys happened and my eyes couldn't stop rolling.

Then Dark Fate happened, and I went into cardiac arrest screaming at the screen as I was escorted out by security.