If logging isn't practical or you want to be more proactive and prevent Private Browsing from being accessible in the first place, it is possible (though not a short process) to disable Private Browsing if you are willing to mess with Safari's internal files. Note that macOS 10.12+ will not allow you to modify, overwrite, or delete Safari.

Feb 06, 2011 How to Turn On or Off Private Browsing On iPhone or iPad Jan 28, 2018 How to Turn on Private Browsing on Your iPad

Turn off Private Browsing (iOS Safari) On an iPhone, iPad, or iPod touch, open Safari, then tap (bottom right corner). Tap Private (lower left corner) to turn private browsing off. While Private Browsing is on, Safari appears black or dark instead of white or gray.

Always open windows with Private Browsing. In the Safari app on your Mac, choose Safari > Preferences, then click General. Click the “Safari opens with” pop-up menu, then choose “A new private window.”. If you don’t see this option, choose Apple menu > System Turn off Private Browsing (iOS Safari) - ProtonMail Support Turn off Private Browsing (iOS Safari) On an iPhone, iPad, or iPod touch, open Safari, then tap (bottom right corner). Tap Private (lower left corner) to turn private browsing off. While Private Browsing is on, Safari appears black or dark instead of white or gray.

Jul 12, 2019

Always open windows with Private Browsing. In the Safari app on your Mac, choose Safari > Preferences, then click General. Click the “Safari opens with” pop-up menu, then choose “A new private window.”. If you don’t see this option, choose Apple menu > System Turn off Private Browsing (iOS Safari) - ProtonMail Support