I have created a backup of my cloud instance.
Then I created a new (!) instance and used that backup.
Now I have this (new) field in ALL projects in the "create Screen":
Where does this field come from? How can I get rid of it?
You are correct in that feature which is causing you to see the status dropdown - this is a fairly recent feature.
Unfortunately I don't believe it is possible to remove this feature, as per this feature request. I would suggest voting for this issue as it looks like there are a fair number of people who are wanting the same change to be made. It does say on the ticket:
"This feature can be disabled at site level. Please contact Support if you wish to have it disabled."
So this may be your best option for now until the linked feature has been implemented