Rather than locked down, they're basically a black box - I think they have their own firmware and hook into the OS and hardware in weird ways (part of the reason why Linux phones are so difficult to make work)

If the NSA wants to ping your phone location or even turn on the microphone, they can, supposedly even when the phone is "off". If they want to side channel load in a rootkit, they probably can

But NSA surveillance comes in two main flavors - broad and focused. If they think you're a terrorist or of strategic interest, there's a lot they can do... But that means actual humans are interested in you, personally.

But for everyone else, they're not going to sift through ten million phone storages - that's way too much data to be useful, and they already have long collected way more than they could make use of. The broad stuff is about flagging people - the most effective is to look at networks of people. If you have connections to a terrorist, you're a potential part of the network, and so you'll be flagged as more interesting. I've heard rumors that certain keywords might be flagged on calls too, who knows. Too many flags and they might devote some man hours to looking into you personally

But generally, they're very protective of their tech. They don't use the good stuff widely, because it's not useful, and it increases the chance for discovery and countermeasures. My understanding is they won't share their surveillance systems either - they might put notes or flags on shared LEO systems or tip someone off, but they really, really, like to play it close to the vest. Even with other 3 letter agencies

So yes, this possibility exists - especially with llms to help filter through this information ocean - but there's no shot they're sharing capabilities with border control agents