Hello Lianna Williamson,
It sounds you are having an issue navigating the YouTube app on your iPhone 13 mini, and we'd like to help. When you tap to minimize the video you are watching, the touch screen is unresponsive, is that right? Has this happened once, or are you having repeated issues with the YouTube app? Is the Touch Screen responsive in other apps?
Try quitting the YouTube app, restarting your iPhone, and launching it again.
If the issue persists, update your iPhone to iOS 15.0.2, which was released October 11, 2021.
If the issue is only happening with YouTube, you may need to reach out to the developer.
The resources below will help you with this:
Close an app on your iPhone or iPod touch
Update your iPhone, iPad, or iPod touch
If the screen isn’t working on your iPhone or iPad
How to contact an app developer.
Cheers!