Looking into it a little more, it seems likely that they are simply using an older version of the Twitch API. Looking at their code, I’m seeing references to Kraken pop up here and there, along with “passport.twitch.tv” instead of “id.twitch.tv”.
I can get Streamlabs Chatbot to trigger a raid by having it post "/raid " when I type in a command, such as "!raid ".
It’s a work around, requiring an external program, and while I’d prefer to do this without it, I think this is the best result I’m going to get.