Hi Dr-Jeckle,
It appears that you're countering a couple issues with your new iPhone 13 Pro, one being that you are seeing a message about an event that cannot be added to a calendar, along with quality issues for photos or videos of people.
Do you only get that message alert when watching videos? If yes, does it happen with any videos you watch or specific videos from a specific app? Do you have any accounts on your iPhone 13 Pro that you sync your calendar or any calendar to? Additional details can possibly help determine what might be going on and next steps. If you haven't already, you can see if restarting your iPhone may help: Restart your iPhone It can seem like a simple step, but it can sometimes help resolve issues. You may also want to check out the following article about brightness and color temperature of your iPhone, which may also help: Adjust the brightness and color temperature on your iPhone, iPad, or iPod touch
Best wishes to you.