When using Safari private mode, when trying to exit private mode to normal Safari browsing the private put-on to disable is not visible. It is visible for a second when opening a new private window but you cannot press it during this short time to disable the feature.
iPhone 8, iOS 14
See the information in Browse privately in Safari on iPhone - Apple Support including the following:
To hide the sites and exit Private Browsing Mode, tap 
, then tap 
to open a different Tab Group from the menu at the bottom of your screen. The private sites reappear the next time you use Private Browsing Mode.
To close private tabs, tap , then swipe left each of the tabs you want to close.
See the information in Browse privately in Safari on iPhone - Apple Support including the following:
To hide the sites and exit Private Browsing Mode, tap , then tap to open a different Tab Group from the menu at the bottom of your screen. The private sites reappear the next time you use Private Browsing Mode.
To close private tabs, tap , then swipe left each of the tabs you want to close.
Private mode disabling.
