No, it's not a web page as far as the API is concerned, although it is indeed built using web technologies. It's also not a content script that you add in the html. Content script is a special kind of script that runs in an isolated world context from a foreign web page. Your extension page is not foreign, it is domestic, it doesn't have an isolated and you wouldn't want one here anyway.
In extension pages you can simply create a new <script> element and set its `src` property to the name of your extension script.
You can even do it from the outside if you opened the page via window.open() or chrome.extension.getViews() if the caller is another extension page (such as the popup/options page) or use messaging (chrome.tabs.sendMessage, BroadcastChannel,
navigator.serviceWorker) if the caller is the service worker.