Okay, I was checking this evening again. for some reason now the old problem is occurring again, although I did not change anything. Inspecting Elements on Desktop and mobile both show the same timeprint after purging the cache, although I have “phone” in Cache Groups enabled and added “mobile”. Could there be just a problem mit Safari/iOS?
Thank you, That helped initially. However, after fixing that and now making a few more changes to the mobile version, the newest version is not getting published. I am sure I am purging my caches everywhere, bit the „Sign Up“ is still in green (for example, that‘s not the only change I made).