Those polls you got your source from are actually polls done by state-run polling facilities. of course poeple are going to say what the state wants to hear. here's a video on it. https://www.youtube.com/watch?v=_uQCNjIHeqU
Btw, by saying that "80% of Russians support this war", you're spreading Russian state propaganda.
And of course protests in Russia died down, people get jailed for like 10-15 years in prison if they protest, so by fear of getting jailed, protestors stop. it isn't pretty but it's how the system works.