Your assumption that a JWT is an OAuth Token is incorrect - JWTs only work as authentication for the Endpoints under the /extensions/ path in the API - not Helix. (See also what is mentioned under Authentication for each endpoint here vs. here)
You’ll have to send the Broadcaster through an additional OAuth Flow to receive the required scopes on a User Access Token.
Feel free to reference the Docs on Authentication or my FAQ Post about it or ask any further questions here.