It was introduced by third-party applications which give multiple people access to a single (or more than one) Twitter account(s). I'm not sure if it was the first to do it, but CoTweet was the earliest that I recall, it would tag tweets with ^CC (initials) based on which CoTweet user account was replying.

Since then it's become fairly standard in customer support, presumably still largely through these third-party apps, but potentially typed manually by some companies as well.

Yep, cotweet was the first app that I saw which seemed to adopt that style

I would say it's extremely common, all Twitter based customer support channels I've ever used have signed off with it.

I thought it was line noise. After all, how does a bot have initials?

Uh they fake them? It looks less obvious this way as when they end with ^unhelpfulbot.

@XboxSupport does that too.