There is also an unspoken bit of realpolitik there: Israel is still an ally to Germany, Palestine isn't, Iran isn't, Hamas isn't, etc.
So this is actually a super-nice position to be in, you can support your ally no matter what they do, while still looking contrite and morally superior by pulling the "we are Germany, we are not allowed to have a say in the matter" card.
Also, Israel is a trade partner, which is important because the non-western countries are hesitant to trade with them. Israel is culturally integrated into certain European institutions, in part due to German support (soccer, Eurovision, other sports).
If this was conveyed more honestly, it would at least be understandable (up to some point).
I think what grates me is the dishonesty: We want to do both at the same time: A neutral mediator that advocates for the two state solution and the world's (second-)closest ally of Israel. That's like wanting to be both the coach and the referee. At some point it just becomes an insult to everyone's intelligence.
It half-way is, at least by the new chancellor Merz, who praised Israel for doing our "dirty work" in bombing Iran. And he was promptly criticized by the rest of the political establishment and the press for that.
Well, let's face it: Nobody likes the current Iranian government, and nobody wants yet another state (especially with a leadership like that) to have nukes. Just that nobody dares to do anything beyond sending strongly worded letters and time-wasting "diplomatic initiatives".
So this is actually a super-nice position to be in, you can support your ally no matter what they do, while still looking contrite and morally superior by pulling the "we are Germany, we are not allowed to have a say in the matter" card.