I have no idea what’s the name of this one.
Edit: Thanks to the info from @rozlav@lemmy.blahaj.zone, this is the Stropharia caerulea, commonly known as the blue roundhead.
Edit2: Another update on what we are looking at thanks to @oftheair@lemmy.blahaj.zone: It might also be Stropharia aeruginosa, commonly known as the blue-green stropharia
So I searched a little bit and according to my mushroom-page of trust it is edible: https://www.123pilzsuche.de/daten/details/BlauerTraeuschling.htm (in german).
There it says, that some people do not stomach it well but in general it does not have an exciting flavor and is best be added to other mushrooms. A bit underwhelming…
I will not eat it. xD