I was in a similar position. My interview was months after the expiration date of the notice due to covid delays. I didn't do anything about it and everything went fine.
You only need a valid green card for Germany (no requirement for 3-months validity after return).
This is a link to the visa processing center: https://usa.blsgermanyvisa.com/
They list all the requirements there.
I see! I think you should wait for the extension letter in that case. My experience is a little bit different because my green card wouldn't expire until a month after my return. (my guess is that they don't care because they expect you to take care of it to be able to come back to the US but that's just a guess. FYI the German consulate is very responsive to inquiries: https://www.germany.info/us-en)