What was the Russian public view of the invasion of Crimea and Georgia or the ongoing conflict in the Donbas, the intervention in Syria, Libya?
Domestic Russia gets fed the narrative that the dictatorship want them to believe - the nasty western sanctions against poor Russia, the evil NATO empire expanding east ready to attack Russia, the need for Russia to help out poor nations being overthrown by the corrupt west and their puppet regimes.
Domestic opinion does not matter to a dictatorial regime with an iron grip on the country
We'll never know because the polls are so ridiculously unreliable, but as you rightly say -- it doesn't really matter (unless they have another revolution!) I gauge my view on it by spending time on their Reddit pages.
I actually went to some of the Greek islands in 2008 when the Russia-Georgia war was taking place. There were a lot of Russians holidaying there and the overwhelming feelings from them were of embarrassment and dread. Some seemed supportive, but they were old enough to remember the humiliation in the years after the Soviet Union's breakup in 91.