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Volunteers, no corps as far as I know.

https://en.wikipedia.org/wiki/Archive_Team

rsync.net donated online storage for the original geocities backup efforts in 2009.

A decent amount eventually ends up at archive.org

[not all, because archive.ort needs to be a bit more careful, but they have a decent symbiotic relationship]

I love archive.org but they have to start becoming a) very careful indeed and b.) better at cleaning up the content that has been uploaded. By this time there is an insane amount of illegal content on it like ripped CDs and copies of books which still can be bought. I don't want them to go down because of this kind of stuff.

It was founded by Jason Scott (of textfiles.com) who works for the Internet Archive (which is nonprofit). So while I think the Archive Team is fully community driven project what they backup ends up on Internet Archive.