There’s no unbreakable secure tooling, none. It might be unbreakable against script-kiddies level of hacking, even though I have my doubts even about that, but Snowden and the general atmosphere during the last decade or so have proved that State actors can put their hands on almost any piece of data out there, either through genuine hacking or other means involving their monopoly on violence.
It’s absolutely possible to verify something anonymously.
Here was an interesting example recently https://help.kagi.com/kagi/privacy/privacy-pass.html
You missed my part about State actors and their monopoly on violence. I think it used to be called the “hammer metaphor” or some such, a not very technical solution, if at all, but more than efficient nonetheless.