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Uh-huh. A connecting link. Terminator 2.5.
But in the third movie, there are no references to the series. As for what happened to John after "being submerged in molten metal," he just lived on until he was a young man. Not surprising, since the series was filmed much later.
And the third movie also has a moral. It's repeated every 10 minutes. But I still didn't understand it, whether "the future is predetermined" or not.
And I liked the third movie. Of course, there are flaws too. In the first two, it's constantly stated that the machines enslaved everyone and drove humans into camps, and then a mystical John appeared, who taught the enslaved people to hit the machines hard in the eye with a shovel. And resistance movements broke out. But in the third movie, at the end, he immediately took the initiative into his own hands.
By the way, did you notice that the third movie is the only Terminator film without scenes of a grim future with Necromancers marching over human skulls?