@pamtbaau I tried it again with Chromium and its Dev Tools Console and the error message was similar, but a bit more concrete. So I googled around and found, that renaming js.cookie.mjs to js.cookie.js could be a solution. So I tried this and updated the importStatement in youtube-consent.js and the asset.addJs Statement in base.html.twig accordingly and now it works!
Thank you very much for your help!!