Hi, thanks for your reply. Actually the message which is visible on your screenshot in the header and in purple background is not the cookies message, it is another one I set to notify visitors that the site is still under development and customer orders are not going to be proceeded.
The message for cookies is in the footer (see it here) and currently it is visible on my iPhone X, but not on the other devices I tested with (iPhone 6S and iPad)… All devices are with the latest software version, not sure why is this…