Looks like there is an option to match all urls:
const scriptObj = await browser.contentScripts.register({
js: [{ file: "/content_scripts/example.js" }],
matches: ["<all_urls>"],
allFrames: true,
runAt: "document_start",
});
source: https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/WebExtensions/API/contentScripts/register