You install the extension to a channel
And view it on twitch instead of in the rig.
The rig will spin up a server to hosts files for you.
But you can use a server with the rig anywau.
Hosting an extension is technically identical to hosting a website.
Since an extension is jsut a website.
The only thing you need to test on Twitch instead of in the rig, is you need some real SSL certs to prevent mixed content issues.
So to view an extension on Twitch just install and activate it to slot, just like you would a released extension.
And to view a vidoe extension (either overlay or component) the target channel needs to be live.