I really doesn't matter with that very old iPad.
Google/YouTube has stopped supporting their older app on 8-10 year old iOS devices, now.
This actually happened at the very beginning of the 2021 year.
So, your ONLY option is to use and view YouTube from a Web browser.
Your 2011 iPad 2 is now 10-years old and considered old and obsolete technology.
Sorry, but this is the reality for ALL 8-10-year old AND OLDER iOS devices now. Especially going into 2021!
Apple ended support for all 8-10-year old iOS devices well over 4 years, ago, in 2016.
Third party app developers abandoned and stopped supporting these 8-10-year old iOS devices nearly 3 years, ago, in 2018.
There are, virtually, NO MORE third party apps available from the iOS App Store, any longer!
Third party compatible apps for such old devices are few and far between, now, in 2021.
Also, that nearly 5-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.
It's 2021 now!
You really need to seriously consider a purchase of a new iPad model OR a much, MUCH “newer” and less expensive, refurbished or used iPad models, from better known, trusted Apple product/device retailers/resellers, locally or online, on the Web/Internet, capable of running the latest iPadOS versions.
There are PLENTY of newer, older iPad models that can run the latest, current versions of iPadOS.
I am sorry that you had to learn all of this, but this does not change any of the facts regarding these very old iOS devices.
Sorry & Best of Luck to You!