You do realize only a fraction of demonstration was arrested, and that for every person who risked getting beaten up and arrested there are many of his friends and relatives who support his views

That's why we have polls and statistics, instead of relying on the "most vocal" and supposedly "most courageous" people that "brave" the streets to protest. I personally don't buy it.

Again, there are no independent institutions or media left who could conduct polls and statistics.

All "polls and statistics" you see are basically fabricated by the government, either directly, or by induced fear.

If you're going to make up numbers, why not make up a majority? Be more ambitious.

10k is absolutely something in an authoritarian country when there is no free speech at all or freedom of assembly. And serious repercussions for those seen as against Putin.

10k is the number of people who were ready to be beaten, detained, tortured, have huge fines and later have their families harrassed.

You cannot claim that the only people who are against Putin are those who took part in illegal protests that are punished with hefty fines and arrests. Not everyone is that brave.

While Putin might have high rating in the polls, his party United Russia could win only 50% of seats in Moscow Parliament in 2019 (after most popular independent candidates were not allowed to be in the ballot). Furthermore, members of United Russia nominated as independent candidates to hide their party affiliation. If you believe that only ten thousands people are against the government then how can you explain this?

Another example is that Navalny was denied to register a political party for many years. If he has only 1% or 2% of supporters, as propaganda claims, why deny registering a party? Let him take part in election and get his deserved 1% with a disgrace (by the way, in 2013 Moscow Mayor election he got 27% of votes and obviously that was the last election he was allowed to take part in).

So from the above facts I can conclude that Putin's support is not absolute. There are reasons why he doesn't allow to hold fair elections, why protests are not allowed, why all major mass media are controlled by the government and Internet is censored. You don't need this with true 80% voter support.

Also urban liberals aren’t representative of the country as a whole

nailed it. That's a bias I'm surprised very few people are able to grasp in the Internets, the same urban liberals ( from any country really ) or higher class tend to favor Western social networks, or be simply pro-Western, thus completely biaising the " I'm [Insert your nationality here] .. blablabla " It's especially rampant on Global South or emerging countries, while the richer people can actually afford slacking on Reddit responding to a mostly Anglophone audience.