Yes, keeping the remaining nuclear plants running would have reduced emissions and electricity prices somewhat. A 2024 Energy Policy study estimates the 2022/23 extension lowered German wholesale prices by about €9/MWh. That's a real effect, but nowhere remotely close to "the nuclear phase-out doubled electricity prices." The huge price spike was primarily the European gas crisis. You know, the one for which LNG terminals had been built.
Nor did Germany replace nuclear with coal. Coal generation subsequently fell to levels not seen in decades, while renewables grew substantially, so German emissions fell as well.
Attributing the nuclear exit simply to "the Greens" is rather selective history. The original exit was SPD/Greens, but after reversing it in 2010, Merkel's CDU/FDP government legislated essentially the final phase-out schedule again in 2011. So basically: every party that was at the levers of power.
You could make a perfectly reasonable argument that shutting existing nuclear before coal was bad climate policy in hindsight, because of the gas crisis. But I don't think you need to resort to the rather dubious claim that it doubled electricity prices as a singular cause.