SPD was traditionally more cooperative towards Russia, they were the ones who signed the deal to biuld Nordstream2. Germany's national bourgeoisie had very clear material incentives to be less hostile towards Russia than the US, and the SPD was a main driver of a cheap gas policy that formed the backbone for that. This is obviously no longer allowed by the US as of now. And yes, the Greens were in coalition with the SPD during the Iraq war and both parties opposed that war - although both also participated in bombing Kosovo and invading Afghanistan. Iraq was a very one-off thing that was probably motivated by the upcoming election back then, nobody in Germany believed in the WMD thing back then, it was widely called out as a hoax in the German press etc.

The Greens used to be deeply rooted in pacifist, nuclear disarm movements during the 1980s when they formed. These were huge in Germany (maybe unsurprising for a Cold War frontline state that had started and lost two world wars). As soon as they came into power on the federal level, the party leadership pivoted to being a warmongering imperialist party that was part of the first German government to send combat troops abroad since 1945. Western Germany was obviously deeply entrenched in the NATO structures ever since its foundation, but mostly as a staging ground, logistics hub, donor etc., citing the country's fascist and militarist past as the reason to not engage in wars with boots on the ground. It was the "red-green" coalition with the Greens under Joshka Fischer and the SPD under Gerhardt Schröder that changed that, at first under massive protest from the party base especially among the Greens. The anti-war crowd is now completely neutralized, today's Greens are by far the most imperialist party in Germany and are the loudest Slava Ukraini stans in the current federal government consisting of the SPD, the Greens and the libertarian FDP. You can imagine the Green stance among the lines of an aggressive V*ushite radlib homonationalism.