The NSA buys most of their zero days. It's no wonder why they have libraries full of them. Finding exploits is a bit different to developing stuff too.

I agree that they have the vast amounts of training data that they could put to use. I would not be surprised if they had a quantum computer that has broken RSA lower bit ranges by now. This was proven in academic circles to be possible and just needed scaling up. The same is true for using wireless emitting devices to see through walls.

I'm almost certain that they have full access into Tor now. I read a while ago that they monopolized many exit nodes. Snowden and others must be using multiple methods to conceal their true locations.

But do they have a self improving AI? I don't think so. OpenAIs main goal is to create a GPT knowledgeable enough that it can help them improve their own models, AKA reaching the singularity - but with human intervention to prevent a run away effect. Transformer based models are not going to give us AGI. Once the researchers figure out what's really needed then govt will adopt and scale it. Until then it's just fancy closed source private versions of what is currently available.