There's just one problem with the "climate lockdown" hypothesis.
When the coronavirus lockdowns were announced, they were explicitly understood to be temporary. It was originally sold as two to three weeks (except in New York, where Cuomo was the first to openly admit he planned to keep the state locked down for months), but the nearest precedent—the Spanish flu lockdowns of 1918 and what we could deduce was coming out of China at the time (as unreliable and propagandized as that was)—suggested that we would be granted our normal lives back by summer 2020. Compliance was built on the premise that it would end in a reasonable amount of time, like all other restrictions in history.
That, obviously, did not happen in most places. The problem was that they never had an exit strategy after contact tracing was proven ineffective. They knew that the moment they lifted restrictions, the virus was going to spread again. And so, like micromanagers on steroids, they decided to forestall the inevitable while, of course, turning blind eyes to rioters, something that undermined everything they said they were doing. They seriously tried to suppress society for over a year until they could rush a totally new, undertested vaccine onto the market. One that eventually failed to stop the spread, just like all other efforts.
With all that in mind, a climate lockdown would have no known exit strategy. It would be permanent. Most ardent believers will admit that the climate is too far gone to stop. It would merely be mitigation, forever, even as the climate warms (slower, mind you, than they say it would without such draconian measures). So with a guarantee that we would never get our lives back, you would have far less compliance. And even if politicians tried to say there would be an end, the experience of 2020 and 2021 would still make such a claim unbelievable.