A twitch extension frontend is all HTML, JS and CSS.
Creating what you describe requires only these things. HTML/CSS to make the blue box.
And a bit of JS to fetch in data from Twitch to convert the TwitchID passed in to the Channel Name.
Extensions are “easy” as they are JUST HTML/JS/CSS. And you just need the ability to make AJAX calls from JS to your server. It’s the same as building a website, just your front end is on a different server to your backend.
A sample extension covering your example would only contain HTML/JS/CSS. It wouldn’t have much else in it that you wouldn’t learn from a “standard” course in web development.