iPad apps not "recognizing" updated software

Your initial post states that you have iOS 10.3.4 installed - and not iOS 13.

If the App requires iOS11 or later, you must update the OS software. It follows that if you do have an iPad4 - as information that you have provided would suggest - update of your iPad is not possible.

Whether or not you are able to update any iPad to a newer version of iOS/iPadOS will be dictated by the iPad model - and the currently installed version of iOS. You can find this information here:

Settings > General > About

Not sure which iPad you have? Identify your iPad model.

Here is a list of the highest version of iOS supported by the older models of iPad (for simplicity - “generations” are shortened to a number) that are restricted in their ability to be updated:

iPad1 - iOS 5.1.1

iPad2, iPad3 and iPad mini1 - iOS 9.3.5 (WiFi Only models), iOS 9.3.6 (WiFi & Cellular)

iPad4 - iOS 10.3.3 (WiFi Only), iOS 10.3.4 (WiFi & Cellular)

iPad Air1, iPad mini2 and iPad mini3 - iOS 12.5.5

Newer models, not appearing in this list, are all able to be updated to the current version, iPadOS 15.4.1

If your iPad is capable of being updated to a more recent version of iOS/iPadOS than is currently installed, these support pages outline both the available methods by which the update can be performed - and troubleshooting should you experience difficulties:

Update your iPhone, iPad or iPod touch – Apple Support

If you can't update or restore your iPhone, iPad or iPod touch – Apple Support

If your iPhone, iPad or iPod touch won’t update - Apple Support

iOS update and restore errors – Apple Support

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 The 32-bit platform upon which the iPad4 is based is obsolete.

Many App Developers have also dropped support for 32-bit devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store.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 Once compatible versions Apps are withdrawn, you’ll not be able (re)download or (re)install them.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 iPad9 supports current iPadOS 15 - and has hardware specifications and capabilities that vastly outperform your old iPad4.

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

You only option is to buy a new(er) device, which can support the current iOS/iPadOS version.

Regards

Giulio