Google has stopped supporting its YouTube app on very old versions of iOS.
You need to use a Web browser to access the YouTube website instead.
You need to realise.
Upgrading/updating that iPad any farther will never, EVER be possible.
If your iPad model has been stuck on iOS 10 for all of these past years, then it is possible you own an over 9-year old, 2012 iPad 4th generation.
That iPad model cannot ever upgrade beyond iOS 10.3.3/10.3.4.
An over 9-year old, iPad 4th gen model is too old, now.
Sorry.
Apple ended support for all 8-10-year old iOS devices nearly 5 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, VERY late in 2021.
This includes apps for both iOS 9 AND iOS 10 devices!
AND, NO WAY to initially install any older, compatible, third party apps into this old iPad.
NO MORE SUPPORT! NO MORE APPS!
AND, that 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 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 ) The ONLY “new-ish” Web browser I recommend for any old/er iPad models at this late timeframe!
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 device, up to date, third party Web browsers today, in 2021.
All 2011-2012 iPad 2, 3, 4 and 1st gen iPad Mini models are fully and completely unsupported AND obsolete!
Sorry, but this is the reality for ALL 8-10-year old AND OLDER iOS devices now. Especially now, VERY late in 2021!
In addition, the internal, rechargeable batteries in these old iPads are, also, running on borrowed time.
Not worth the costs to replace these old internal, rechargeable batteries in these old iPads, any longer, either.
It's VERY late in 2021 now!
If you need/want an iPad with an up to date iPadOS with access to current, updated apps, then 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, some locally or from online, on the Web/Internet, capable of running the latest iPadOS versions.
There are PLENTY of less expensive, newer, older iPad models that can run the latest, current versions of iPadOS.
If you need OR ONLY able to purchase older, less expensive iPad models, look at older IPads from 2014 and later.
All of these older model iPads, below, CAN run the latest releases of iPadOS 15.
2014, 9,7 inch screen iPad Air 2 models
2015, 7.9 inch screen iPad Mini 4 models
2015-2017, 12.9 inch screen iPad Pro models. ( 1st gen Pencil support )
2016, 9.7 inch screen iPad Pro models ( 1st gen Pencil support )
2017,10.5 inch screen iPad Pro models ( 1st gen Pencil support )
2017, 9.7 inch screen iPad 5th gen models
2018, 9.7 inch screen iPad 6th gen models ( 1st gen Pencil support )
2019, 10.2 inch screen iPad 7th gen models ( 1st gen Pencil support )
2020, 10.2 inch screen iPad 8th gen models. ( 1st gen Pencil support )
2019, 7.9 inch screen iPad Mini 5th gen models ( 1st gen Pencil support )
Get the largest internal data storage model you can afford as NO Apple iOS device has ANY expandable storage.
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!