Yeah - ultimately, the ideal way to do it would be to have a server set up where your extension routes through, and the server gives the response to the extension but also caches it - so if any other extensions make the same call within next few minutes, they get it straight from your server, rather than polling Twitch API again.
Something along those lines would help as even if you have, say, 500 users, you can start running into the same problems.
I don’t run anything large scale though so my insight is limited to regurgitation 