One would assume that OBS has an agreement with Twitch since it’s one of the largest options for streaming on Twitch. (or a temprorary “we’ll allow this until you can make changes”)
Really everyone should be doing everything via the API’s as supported using the relevant access tokens.
Just ease of use for OBS to be able to dock in various widgets.
But for your “chat bot app” you probably don’t need a chat box to show chat (or send chat via that), and just need to display what the bot sees, so you probably don’t need to embed widget. Just get a correctly scoped token and utilise that.