I wonder how much of this is traffic caused by peoples agents using web tools causing searches and fetches rather than general trawls of the internet.

Very little of it. When you see a million IPs systematically working their way through your URL space, it's pretty clear that there's a central control node behind it all.

Most well-known/large agentic web tools I've seen are actually super honest about who they are -- even when they write out scripts they're very keen to identify themselves using user-agents. Most of the time those tools are fine - it's the ones that happen to have a random choice of the 5 most common Chrome/Firefox user-agents making sequential scrapes but cycling through IPs on African and South American residential IPs that are the problem!

I've seen some logs where a bunch of random ips were hitting a client's search endpoint feeding what looked like user questions to it. Of course none of them returned anything useful but it was causing a lot of strain and even causing the site to go down (gotta love wordpress's stock search).

I'm guessing the training companies are taking real/synthesized user queries and trying to distill what they can from site searches.