The NSA collects and archives all internet traffic it can access for future analysis. It's the purpose of the Utah Data center.
Think about it. The Internet runs on tens of thousands of massive datacenters. Thousands are being built as we speak. Obviously a single datacenter cannot hold an appreciable fraction of that.
BTW, the total budget of the NSA is less than the R&D budget of a FAANG company, so if you find yourself believing that they might have alien-level technology far beyond Google and AWS, you’re watching too much TV.
https://en.wikipedia.org/wiki/Room_641A
Public information shows that the NSA has been active intercepting as much data as possible.
It doesn't require the budget of a FAANG to peek through a significant volume of internet data.
"The Internet" would require 1000 times less servers if it wasn't running off Python scripts in Docker containers in VMs in a virtual overlay network. (I'm exaggerating these numbers only slightly.)
I think spying on traffic is just a massively simpler task than generating content.
I would suspect that today they also process the traffic for llms and thus store a bit more of the traffic as weight and biases. All that can be done distributed and to different degrees based on how much access they got and under what operational conditions.