If you just need to know when a streamer is live or not then Webhooks would be the best option as 6k subscriptions is within the max subscriptions limit and would result in less useless data (as when polling a large portion of the time you’ll just be getting back the same data).
One thing to note though is that for 6k users polling wouldn’t be too many requests, you can check 100 streams per request so that’s only 60 requests, which is easily viable to do up to once per minute. That being said though I’d still suggest using webhooks.