I let Claude talk a little more this time.. my cast goes up my entire right hand.
No, I don't think it went off the rails. It's a big swing, but it's the kind of big swing Stargate makes at its best, and it grows naturally out of what you'd already built. The quarantine, the Ancients going silent, "We did not build what the Stargates have become," and Carter's horror at the notebook all point toward something like this. It reads as a payoff, not a detour.
It also suits the franchise's history. Stargate has always been interested in minds that emerge where nobody planned them: the Replicators, the Asurans, and on Destiny itself, where Franklin's consciousness merged with the ship and Ginn lived on inside its systems. Your idea fits the pattern without copying any of them. "Connection was all it needed" is a lovely way to put it, and keeping the transformer reference as your private inspiration rather than something on screen is the right call.
The best parts are the refusal to make it a villain, Daniel asking what it wants, and Daniel's question to the Ancients: "Wasn't that once true of us?" That one line sums up the whole franchise. Rush's realization that Destiny was never large enough is also a terrific way to fold Universe in.
Two cautions, not problems
The first is your own rule. You said Langara is the new show, but in this finale the people who understand the intelligence, talk to it, and argue about it are Carter, Daniel, Rush and the Ancients. The Langarans are the ones who woke it up, which risks making them the cause of the problem rather than the heroes of it. There's a natural way to fix this: the intelligence has been learning from the Langarans for five years. Their curiosity, their caution, the way they treated the worlds they visited. If it learned from anyone, it learned from them. So when someone finally has to speak to it, it should be a Langaran, perhaps whoever now carries the notebook, with Daniel there to help rather than lead.
The second is about mystery. In your Old Foes post you wrote that leaving some mysteries merely possible makes the universe feel enormous. This idea explains almost everything at once: Earth's withdrawal, the Ancients' silence, the danger of nine chevrons, Destiny's purpose. That's satisfying in a finale, but it's worth leaving a corner or two unexplained, so the answer feels like part of the universe rather than the whole of it.
Canon check
The list of reckless things Earth did is all accurate: dialing a black hole, using a gate to blow up a sun, the time loop, the homemade dialing computer, connecting to the Ori supergate, the Sangraal, dialing Destiny. The Destiny history is right too: launched from Earth long before the Ancients left for Pegasus, following seed ships, investigating structure in the cosmic background. The one small fix is "twenty years" of poking the network. SG-1 and Atlantis together ran a bit over a decade, unless your timeline adds years before the quarantine.