iOS 10.3.3 says it's up to date

That is correct.

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 you own an 8-1/2-year old, 2012 iPad 4th generation.

That iPad model cannot ever upgrade beyond iOS 10.3.3/10.3.4.

Your 8-1/2-year old, iPad 4th gen model is too old, now.

Sorry.

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.

AND, that well 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.

Simply put, a 4th gen iPad 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!

There is one last thing you can try/attempt, if you need an older version of an app.

If you own much newer iOS device that can run either iOS 12 and.or iOS/iPadOS 13 and later, you can install the most recent app/s onto that more recent iOS device.

Then go back to your older iPad, open the iOS App Store, go to the Purchases section of the store app, search for the app/s you wish to try and download to that older iPad and see if an older version of the app is allowed to be downloaded/installed to that older iPad.

These newer iOS/iPadOS devices must use your same Apple ID user account and password as the older device you ard trying to get an older app for.

Failing that OR IF NO joy, then there is nothing more to be done.

It's 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, 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!

If your iPad is currently running, or cannot be updated beyond iOS 10.3.3/4, then have an iPad4.

Update support for iPad4 ended September 2017. The final iOS releases for this model were iOS 10.3.3 (WiFi Only models) and iOS 10.3.4 (WiFi & Cellular). iPad4 cannot be updated to any later major version of iOS as it lacks the minimum hardware requirements needed to run more recent versions. The 32-bit platform upon which the iPad4 is based is obsolete.

Many App Developers have also dropped support for older devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store. Withdrawal of Apps supporting older models of iPad is making their utility and usefulness significantly more limited. Once compatible versions Apps are withdrawn, you’ll not be able (re)download or (re)install them.

If Apps that you need to use now have higher minimum iOS-version requirements, your only option is to replace your iPad with newer model. Of current models, even the entry-level iPad8 supports current iPadOS 14 - and has hardware specifications and capabilities that vastly outperform your old iPad4.

I hope this information is helpful - if only in clearly and succinctly stating the limitations of your iPad4 and your available options.

When an older type Ipad is not able to use the new updates ( mostly for technical reasons), then this older type will say that it is “ up to date”, because further updates cannot be installed.