Your iPad Air2 can itself only be updated to iPadOS 15.4.x. This model does not support iPadOS 16 or later - at the time of writing, iPadOS 18.4.1 being the current version.
Many third-party App Developers support only the current and perhaps one or two earlier major versions of iOS/iPadOS. That said, the available YouTube App requires iPadOS 15.0 or later, and as such, should be compatible with your iPad if you have updated the iPad to its most recent supported version of iPadOS.
If specific Apps that remain compatible with your older model iPad are not functioning as expected, try deleting and reinstalling the App. If the problem persists, you'll need to seek assistance from the relevant App Developer:
How to contact an app developer - Apple Support