Data ingress is usually free, which really cuts down on costs when scraping. If you can do everything in-memory, it's surprisingly cheap. The important bit is being respectful of robots.txt files and not overloading small sites with too many requests.

I have a background in scraping from prior projects over the last decade.

Bandwidth is not a concern for projects like this at a lot of hosting/VPS providers.

Yes, I did expect they meant HTML served over HTTP(S), although not all documents are HTML and not all internet communications are "the web", and even among those that are HTML served over HTTP(S) and available on the internet, many might not be found so easily. It does need to be mentioned better, because "the entire web" still seems not specific enough; even if it is only HTML over HTTP(S), exactly which documents are found? (I also think it strange they say they monitor "the entire web plus social networks". Most (maybe all?) social networks are web based, and even if they don't, they don't specifically say which ones.) (Still, also note that IRC logs are sometimes available over HTTP (in which case presumably they are still going to be found), but sometimes they are plain text and not HTML. Plain text documents are used for other reasons too.)