Yes, it's a JS-heavy website with a webdesign that makes my eyes hurt. Sigh, can't have nice things, can we?
You can skip right to the signing by going to the relevant Citizens' Initiatives website on europa.eu here:
https://eci.ec.europa.eu/038/public/
Both sites seem to work fine in a Tor Browser, and the signing requires solving a self-hosted captcha (no Big Tech captcha involved, it seems), so at least that's good.
@rysiek: of course I mailed website owners regarding this situation.