That's the real issue right now, the people can do all kinds of civil disobedience, but as long as the police just rounds them up and arrests them by the thousands it won't change anything.

I wonder what it'll take. Given that currently the Russian economy is getting decimated, I wonder if it'll take a few weeks or months of not getting paid. But that might just make them more ruthless and make them start extorting people for money, since they still hold power.

In previous eras pay was highly correlated with the ability to project force, since keeping those parties happy was what kept a ruler in power. Given that Putin rules like a petty feudal lord I imagine a similar principle holds here.

If police stop getting paid, while having to battle thousands of protesters each day, I expect their loyalty to change very quickly.

Exactly, and not just the police. Some 20-30% of the population are actively supporting the current regime and will stand for it. Even if all state propaganda magically disappears and gets instantly replaced by the West propaganda, it'll take months and months for them to change their stance. People hate being wrong, and even more they hate admitting being wrong.

It is a civil war kind of situation we're talking about.