Here’s an interactive map so you can see the percentages better. They are only winning the eastern cities with 21-25% while in the western cities they’re getting 12-15% , so it’s not like there killing it in Berlin and doing nothing in hamburg. If you compare it to 2021, they’ve made just as much gains in the western cities as they did in the east.
I’d say it’s more about the poorer areas wanting a change either with the afd or linke/bsw. Most of the tankie elements of der linke have signed onto the bsw, so pining for the good old days of the gdr isn’t really their selling point anymore. Unless you were just pining for the higher social security and not the authoritarian state or russian domination, which is a lot of people in the east. This split is also part of the reason for their gains in the West as more left leaning people who are hesitant to be associated with the old school communist now have a party.
From what I hear the greens are pretty centrist. Like the democrats in the u.s. but with more of an emphasis on sustainability, but slowly and progressively. They tend to want to preserve the existing social safety net but not expand it like a more left wing party would, or substantially raise taxes on the wealthy. Foreign policy they’re pro Israel and pro Ukraine, as opposed to a lot of left parties that are split on Ukraine but more solidly pro palestine.
They cater to the educated middle to upper middle class urban liberals who want to see some progress on climate changes, which is less of a radical stance outside the u.s., but don’t want a radical shake up in the economic system.
You can check out there German Wikipedia page, most browsers will translate enough to understand these days.