You can always use a Web browser to access the YouTube Website and log into your account there.
The app is just a portal to the actual Website anyways.
AND, that over 4-year old default iOS Safari Web browser is too old, not secure and not safe to use to access the Internet, any longer.
There are virtually NO MORE third party Web browsers left for 8-10 year old iPads!
Available and more popular third party Web browser choices are pretty much GONE, now.
If you must use these old iPad models, here is what is left for still updated Web browsers.
Pickins’ are slim, now!
ALook Web browser ( A fairly new Web browser primarily designed for old iOS device versions, but is still available to newer iOS/iPadOS devices, as well )
Dolphin Web browser
Maxthon Web browser
TOR private browser
TOR + VPN private browser
Turbo VPN private browser
This is pretty much it for iOS 9/10 compatible, third party Web browsers today.
You can easily access the YouTube Website from a Web browser and simply log into your YouTube account that way.
Good Luck to You!