The Greens are more socially progressive than conservatives but it's wrong to think of them as ideological leftists. They arose out of the counter culture movement but they generally stand for a very individualized view of "climate protection".

On a federal level, the Greens are an extremely mixed bag. The Greens in some lands (states) are very progressive and in others they are extremely conservative, especially in the South.

The "moving to the center" narrative mostly goes back to the red-green coalition under Schröder which saw the Greens abandoning their pacifist rhetoric after 9/11 and supporting the SPD in implementing EU liberal market reforms like the massive cuts to the social welfare system. But in principle, this was as much the SPD abandoning its principles as the Greens. Both parties were already in power, so this had nothing to do with appealing to a broader electorate (which is also known to be a false idea: it's not that the electorate won't vote for people too far from the "center", they just prefer voting for candidates they trust to follow through on their promises and most attempts at off-center messaging from so-called left-wing parties tend to be empty promises).

This actually resulted in the split of the SPD with most of its actual left wing leaving the party to later join ranks with the East German PDS (the successor to the East German state party) to form Die Linke ("the left"). But they're their own can of worms so I'll leave it at that.

Regarding Fukushima: while the Greens certainly helped start abandoning nuclear power, Fukushima was the final nail in the coffin and had Merkel (a conservative without involvement from the Greens) cash in on the public reaction to the disaster by publicly stating that all remaining nuclear plants would be shut down on and announcing a timeline. Chernobyl heavily factored into the general anti-nuclear sentiment but it originates with the peace movement (which later tied into the Greens) which frequently conflated nuclear power and nuclear weapons.

I actually think the recent decrease in unpopularity (because calling it "popular" seems misleading) of nuclear energy has more to do with German politics being less haunted by the looming threat of nuclear annihilation that was felt during the Cold War and with more people understanding the climate crisis to be a real prospect and emissions to be a more direct problem than nuclear waste storage. I was a kid in the 1990s but I remember hearing more then about the risks of nuclear power and the dangers of nuclear waste than in the past decade since Fukushima.

That said, if you want a barometer for public opinion it's probably better to look at the headlines of the newspapers BILD and Welt as they shape a lot of the public conversation despite being thinly veiled right-wing outrage bait (BILD being more yellow press and low brow with Welt trying to appear more respectable but ofen recycling the same material). They're both owned by Axel Springer, the German equivalent of Rupert Murdoch.

I don't think nuclear is off the table completely but it's really hard to rekindle because even prior to the exhaustingly slow shutdown of nuclear plants the popularity of anti-nuclear messaging prevented any serious investments in the technology even though this made the few aging reactors increasingly more dangerous while keeping nuclear energy as a whole less efficient than it could have been. We'd basically need to start over. While this isn't in itself a bad thing, it just means any attempt to go back to nuclear would take years before seeing any positive result, allowing for plenty of time to get outraged about nuclear waste storage again.