Should I upgrade my iPad Air 2?

If your iPad is showing a message that you need to upgrade to a higher version of iPad OS, then by all means do it, it brings a lot of security updates and keeps your device and data safe, even if it's just used in a kiosk.

I don't think it'll slow down the performance to be honest. and as a cyber security professional, I always keep all my devices up to date no matter what.

iPad OS 16 is compatible with iPad Air 3 and later, so probably you don't have iPad air 2.

iPadOS 16 - Apple

In being prompted to update to iPadOS16, you don’t have an iPad Air2. The Air2 is only capable of update to iPadOS15 - the most recent version being iPadOS 15.7.3.

As your iPad has an direct internet connection, you are strongly advised to update from iPadOS 14.8.1 - as the current supported version of iPadOS includes essential security updates. Until updated, your iPad is exposed to avoidable security vulnerabilities and exploits. The only argument against updating your device is compatibility with a business-critical App that is known to be incompatible with iPadOS16.x; this doesn’t apply to your Square PoS App.

Given that your iPad is capable of update 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

Be aware that while an iPad may be capable of update, in some circumstances you may need to use a computer to perform the update. To do so, you will need access to either a Windows PC (with iTunes for Windows installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of MacOS). Ensure that your installed version of iTunes has been updated to the most recent version; the essential device drivers are included.

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Update software on iPhone, iPad or iPod touch in iTunes on PC - Apple Support

If you have a beta profile installed, ensure this has been removed from your iPad - as, otherwise, installation of production software updates may be inhibited. This support page provides the necessary information to remove the beta from your iPad:

How to uninstall iOS beta software - Apple Support

You should note that for your iPad to install an available update, its battery must be charged to at least 50% capacity - and/or be connected to its Power Adapter. Similarly, the iPad can only be updated over a standard WiFi connection - or be updated by a PC or Mac using iTunes or Finder - over a USB connection.

if it want to update to ios16 then it's not an ipad air 2

because it max out at

Current: iPadOS 15.7.3, released January 23, 2023

iPad Air 2 - Wikipedia

if it works for your needs then I would leave it be