The answer is so simple it's brilliant: you need a permission from the local police in order to organize a protest on a specific location at a specific time. In most of the cases, that works fine.

In a small number of cases when the authorities really don't want you to organize a protest, they'll keep denying you one location after the other using bullshit excuses until the date when the protest is set to happen. Then they can crack it down for "unlawful assembly".

Note that I'm not from Russia, but I am from a country that looks up to Russia for some forsaken reason and we have experienced protests getting killed in this fashion.

> you need a permission from the local police in order to organize a protest on a specific location at a specific time.

Correction #1: from a town administration, not a police.

Correction #2: the actual legal state of a non-permitted demonstration is fuzzy because while the right for it is given by the Constitution, organizers and any violations of "peace and unarmed" way could be penalized due to federal laws which are stated applicable by the same Constitution.

Is this a serious question?

Even if one ignores the obvious Russia-specific answer, there are plenty of reasons for a protest to be illegal in more western states. Normally it would be illegal to assemble on private land without permission, for example. And there are often laws requiring protests to eg seek permission for a planned route and stick to it (though these may not necessarily be enforced).

Arranging such events must still be legal and people should hear of them and decide for themselves whether they would like to participate. Even “illegal” gatherings are important for a democracy. Perhaps more so than legal ones.

I can’t imagine advertising assemblies without permits is illegal in many democracies?

A protest itself may or may not be illegal, depending on the country. The video of it, on the other hand...

A video encouraging people to participate in an illegal gathering could in some jurisdictions be considered a form of incitement.

Whose responsibility is it to filter content? It seems the Russian Federation wants Google to interpret the law instead of courts.

Perhaps you missed the bit where authorities said that "YouTube advertising instruments" were used to "disseminate information about unsanctioned (unlawful) mass gatherings”?