The currently available YouTube app on the App Store requires iOS 15 or later. Because iOS 9.3.5 devices cannot be upgraded to this version, the official YouTube app cannot be installed in the usual way.
Then, the thumbnails loaded.
Apple’s App Store requires a minimum iOS version for apps. YouTube has long moved beyond iOS 9, and the official App Store no longer serves old versions of apps unless you have previously "purchased" them. youtube ipa file for ios 9.3.5
If this doesn't work, or if you get an "unable to purchase" error, you will need to look into jailbreaking. Method 2: Installing YouTube IPA on Jailbroken iOS 9.3.5 The currently available YouTube app on the App
If the app remains broken, the most stable way to watch YouTube on iOS 9.3.5 is through a mobile browser. Apple’s App Store requires a minimum iOS version for apps