- Do you mean
The viewers each individual delay to the stream content (ignoring Streaming software/Get Channel Info delay)
hlsLatencyBroadcaster from onContext - Extensions Reference | Twitch Developers
- Or do you mean
The delay from Get Channel Info - Reference | Twitch Developers
You can only get the delay from Get Channel Info, using an oAuth token provided by the streamer. So you would need to ask the broadcaster to (re)authenticate outside of the Twitch Extension hosted on Twitch, in order to grant this permission, IE an oAuth flow on your server. Which is what I do for “free cost” EventSub for my extensions, example:
This button goes to my server (the same one where the EBS is) and runs an oAuth flow. I don’t store the result token since I don’t need it I just spool up eventsubs
An Extension JWT nor an Extension helixToken is an appropriate authentication method here for this endpoint since neither represent the broadcaster
- or do you mean
The delay set in the streaming software by the streamer
There is no way to get that via the Twitch API(s)
TLDR
The optimal approach for an extension is just to use hlsLatencyBroadcaster theres no real need to get the streaming delay, since in 99% of cases, streamers do not use the functionality, unless streamers are involved with a competition that requires it, and then every streamer should be using the same delay and you can hard code that on the EBS side.
And in cases where you need it, it’s more benefial to ask the user what their delay is and let them set it in the config view, then this accounts for all kinds of streamer delaying video. (Either in software or in Twitch)