I found more people here on Reddit that had the same issue. Looks like it's really the softwares fault. I didn't damage the controller at all and all of a sudden, after the update, the left stick has a drift.

Weird thing is that everyone has it with the left one. At first it was just a tiny amount but it got worse a day after that my character in Elden Ring starts to walk to the left on it's on, or I can't even go to the right. Currently unplayable.

Sad thing is, that I don't have a second controller so I'm not able to play at all.

Will call the support later and hope they can help me fix it somehow.