If an app like YouTube is stating you need to upgrade their app and the app requires a higher iOS version and your iPad cannot upgrade to that version, then there is nothing to be done, except to purchase a new or much newer, “used” iPad model capable of running the newer version of an app!
Your model iPad Mini is now fast approaching 9-years old noe.
A LOT has happened with iPad in almost 9 years!
If you have very old iOS devices that are 7,,8, 9, 10 years old, then yes, it can get expensive to replace, but these devices are ONLY going to work and be supported, at the most, to up to 7-9 years!
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!
None!
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.
Simply put, your iPad Mini is too old and obsolete now.
Sorry, but this is the reality for ALL 8-10-year old AND OLDER iOS devices now. Especially going into 2021!
Your old iPad has reached its useful limit.
As far as the YouTube app goes, you CAN simply use a Web browser to access the YouTube Website instead of using the app.
The YouTube app is just a shortcut to the actual YouTube Website.
I would NOT use that very old iPad/iOS Safari Web browser, any longer!
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 )
Dolphin Web browser
Maxthon Web browser
TOR private browser
TOR + VPN private browser
Turbo VPN private browser
This is pretty much it for remaining iOS 9 compatible third party Web browsers.
Technology marches on and if you cannot afford to keep up with it every 5-8 years, or so, the old 8-10-year computing technology you own is going to stop being supported within a 10 year period and will NOT be able to function.
It is what it is.
Your iPad is too old.
Sorry.
Today, now in the year 2021, you really need to seriously consider a new iPad model OR a much, MUCH “newer” and less expensive, used iPad models, from better known, trusted Apple product/device retailers/resellers, locally or online, capable of running the latest iPadOS versions.
There are plenty of newer, older iPad models that can run the latest, current versions of iPadOS..
There have been A WHOLE LOT of changes in iPad and iOS in nearly 9 years!
Sorry & Best of Luck to You!