If you are using an iPhone 6, 6s, 7, or even an original iPhone SE, iOS 13/14 struggles with the current YouTube app. Version 1257 was optimized for iOS 13-15. It lacks the heavy JavaScript bloat of modern versions, meaning:
: Tap the YouTube app icon in the search results, then tap the "Get" button next to it. If prompted, enter your Apple ID password or use Face ID/Touch ID to authenticate the download.