I used to think that this was not possible but I recently saw that Testim has an extension that does this.
Core aim: Add a message in the page which doesn't interfere with the DOM/CSS of the existing page.
Chrome/Chromium injects "The browser is being automated" message in the page when the browser is run from puppeteer. But as I understood, this isn't an editable message. How is testim able to do this?