Hello TamishaM,
Does this happen with every video you view, or only some of them? Go to the following YouTube video and see if it will allow you to view it in full screen: iPad Pro — Float - YouTube.
In the example photo you provided, it appears you're trying to view episodes of The Fresh Price of Bel-Air, which hasn’t aired on television since 1996. If you're able to view the iPad Pro video from Apple's YouTube channel in full screen, and the issue is only present with specific shows like The Fresh Prince of Bel Air, this my be happening due to aspect ratio. Some television shows and films were not originally filmed in an aspect ratio that would allow newer devices to view them in fullscreen. It's possible to even experience this with newer content on YouTube, Netflix, and other platforms as well. Netflix does a good job of explaining all of this on the Help section of their website here: Why am I seeing black bars on the movie or TV show I'm watching? - Netflix.
If you're experiencing this issue with every video, including the iPad Pro YouTube video, I recommend backing up your iPhone and restoring it as new next. You'll find steps on how to do that in these support articles:
Once you've restored your iPhone, set it up as new and then test to see if you're able to view videos in fullscreen. After that, you can then restore your content back to your device using the steps here: Restore your iPhone, iPad, or iPod touch from a backup. Test it again after you've restored from your backup.
Cheers!