My new iPhone was not fully established after migration. What are the icons below status bars in right upper corner? How to fix It?

The icons below the battery, wi-fi, and cellular signal level icons are to indicate the Control Center. Swipe down from that area to open Control Center. The Control Center icon will only display for awhile (a few days or weeks if I remember correctly) on a new iPhone.

That is showing you that you can slide down from there to open Control Center.

Swipe up from the bottom.

I believe that is to show how to swipe down for the control center from the lock screen. Once you’ve swiped to get the control center, the icon should stop showing.

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