Sure EventSub would world.
Bits/cheer events are sent to
- chat
- pubsub
- eventsub (either transport)
To send a HTTP request, the optiomal solution is the following, in my opinion.
You use EventSub Webhook Transport
When a Cheer event occurs Twitch will send a HTTP POST request to your Server.
You process that response and then make a HTTP request to your other thing with the required format.
For this use case you just need an Application.
An Extension si for when you want to add an iFrame to a Twitch page to add functionality. And that doesn’t seem to be what you need