> I don't understand. What is Google Search Console, and should I add all my domains there right now?

Google's way of tying real identifies of people to domains, without making it explicit.

Basically, your domain will be weirdly treated by a bunch of entities, none the less Google themselves, if you don't add your domain there (or some other Google property).

Especially with less common TLDs, like .online, they really want to be able to tie it to some identity, so unless you add it there, eventually your domain ends up on some sort of blacklist, in the case of the author it seems they used the "Google Safe Browsing" blacklist to get the author to involve Google somehow.