It's partially true, considering the other two parties were pushing for it too. They
had to agree. Plus, we should not mix Habeck with the Greens. Habeck is an individual that sometimes is not supported at all by his own party.
I still remember the discussions - they were literally the only ones not wanting to do it - they set hard conditions, red lines etc. Obviously this went against their political program - thus the resistance.
It was FDP that pushed for additional extensions. [0]
They even proposed to buy new fuel (and further extend) but no, of course not.[1]
PS: CDU/CSU did what unfortunately was hyped on TV - fear of 3 headed monsters etc. Greens, on the other hand, don't understand that we have an energy issue right now and extending nuclear reactors for another 5 years would buy us some time. The ideology won. The sad irony is that because of this ideological choice, they had to burn more coal....!!!!
EDIT: just found this [2]. What's more to add. They are admitting they could have kept the reactors open for another 15 years.
EDIT: according to Habeck, it was the chancellor that pushed for the extension. [3] confirmed also here. [4]
So all the Greens actually did was resistance.
[0]: https://www.euractiv.com/section/energy-environment/news/ger...
[1]: https://www.dw.com/en/german-greens-lay-out-nuclear-power-po...
[2]: https://greennuclear.online/@collectifission/112588204256628...
[3]: https://www.zeit.de/wirtschaft/2024-06/robert-habeck-akten-a...
[4]: https://www.cleanenergywire.org/news/german-chancellor-decid...