For YouTube forget the app.
You may still be able to access YouTube and your YouTube account using your Web browser, instead.
There are no more compatible third party apps and Web browsers for your 13 year old iPad model.
That older Safari Web browser may, or may not, be too old old to access certain types of Website, as well, and may also, not be safe nor secure enough to use online with today’s modern Internet and Web security protocols.
Also, 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.
Also, these very old iPad models have NO real trade-in nor any resale value, either.
Sorry.
You need to consider that it is nearly the Fall of 2023.
iPadOS 17 is here.
Your iPad model is, now, seven OS iterations behind, 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 sources, like other 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 newer, older iPad models that can run the latest, current versions of iPadOS.
If you need OR ONLY able to afford to purchase older, less expensive iPad models, look at older IPads from 2017 and later.
All of these older model iPads below CAN, currently, run the latest iPadOS 17.
2017, 12.9 inch screen iPad Pro models ( 1st gen Pencil support )
2017, 10.5 inch screen iPad Pro models ( 1st gen Pencil support )
2018 11 inch or 12.9 inch screen iPad Pro models ( 2nd gen Pencil support )
2020 11 inch or 12.9 inch screen iPad Pro models ( 2nd gen Pencil support )
2017, 9.7 inch screen iPad 5th gen models ( NO Pencil support ) (up and coming iPadOS 17 NOT supported )
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 )
2020, 10.2 inch screen iPad 8th gen models ( 1st gen Pencil support )
2021, 10.2 inch screen iPad 9th gen models ( 1st gen Pencil support )
2018, 11 inch or 12.9 inch screen iPad Pro models ( 2nd gen Pencil support )
2019, 10.5 inch screen iPad Air 3rd gen models ( 1st gen Pencil support )
2021 10.9 inch screen iPad Air 4th gen models ( 2nd gen Pencil support )
2019, 7.9 inch screen iPad Mini 5th gen models ( 1st gen Pencil support )
2021 8.3 inch screen iPad Mini 6th gen models ( 2nd 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 old iOS devices.
Sorry & Best of Luck to You!