There is no evidence to be had. Evidence obtained from a public too scared to even be on the street with a blank piece of paper is not likely to be representative of actual opinion. It's not 'they must be', it's 'they absolutely are' - with demonstrated reasoning which has been depicted on TV.You don't get it do you?Yeah, I get it. You don't have any evidence, but you have an anecdote.
We are talking about a poll in Russia, someone calls you on the phone and says 'Hello, my name is Don, I work for the Levada Centre, which is totally independent of the KGB, FSB and the rest of the Russian Government. I am just wondering if you can answer some questions about the government?' - The response you will near always get is 'I think our man Vladimir Putin is the greatest, most trusted leader on Earth'. To people that have seen their fellow citizens arrested in the street for simply carrying a blank piece of paper, what else are they going to say? It doesn't matter who the person on the other end of the phone is, it doesn't matter how trusted and independent the company they claim to work for is, you already know you cannot trust anyone.
It comes as no surprise to any of us that live in the real world that opinion of Putin has increased since the invasion of Ukraine, over night conveniently coinciding with that event it became literally illegal to use the word 'war' in Russia, a protester on the street with a blank sheet of paper was arrested, broadcast on the TV. If someone was almost brave enough to state they didn't think Putin was great, they're definitely not going to be brave enough to say it after that.
It's farken simple logic, and disturbingly, as much as you hate me to point out, it says quite some about your grasp of logic that you, after repeated attempts to explain it, still don't get it.
An independent research organisation comes up with a result that you don't like and you say "it must because they're frightened of being persecuted - which is why they say they love Putin".
If you don't have any evidence then just say so.
Even the Levada Centre has been 'in trouble' with the Russian government, even if I trusted them I wouldn't be telling them anything anti Putin because if they publish tomorrow that Putin is unpopular it's entirely likely the offices will be raided and their phone records confiscated - that is how these governments work. Travel to DPRK, see if you can find a single person willing to speak against their Dear Leader.
You clearly have never experienced living under an authoritarian (or communist) regime. I just asked my father in law as to before Poland was a free country if could he have ever told someone he did not know that he didn't support the government. He looked at me like I asked him if he ever went to school, and said 'of course not, I have told you such things about the Esbek, you only agree with such governments'.
Soooo, Poland is a free country now, and I can ask him what he thinks of the current government, so I said 'Your current government now is terrible right?' and he said 'Kurwa tak!' - I'll let you translate that.
Russians know about and remember Alexander Litvinenko, brutally poisoned in England for essentially speaking out against Putin, now sure, Putin is unlikely to have regular Russians poisoned in such a way, but also know Alexei Navalny, and right now exiting Russia is seemingly harder than going to prison.