iPad 6th generation won't download and update at iOS 16

Begin by ensuring that you don’t have beta profile installed. If a beta profile is present, 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

If the iPadOS 15.7.1/16.1 update still doesn’t appear, perform a forced-restart of your iPad:

Force restart iPad (models with Face ID or with Touch ID in the top button)

If your iPad doesn’t have the Home button, do the following:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. When the Apple logo appears, release the top button.

Force restart iPad (models with the Home button)

Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.

After the iPad restarts, look again for the update.

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

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 Window 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

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.

What iOS/iPadOS version is this iPad, currently, running? Your iOS/iPadOS version maybe too far behind in iOS/iPadOS versions.

What is the rated, internal data storage space/capacity of your iPad model and how much of this free, internal data storage capacity is left inside of your iPad model?

All of that additional info can, also, be found in the Settings app, General settings panel, About.

Your iPad needs sufficient free internal data storage space. At the very least, 7-8 GBs or greater internal, free data storage space.

Is your iPad using a VPN? You need to, temporarily, disable the VPN.

Is your iPad running an iPadOS Beta version? You need to remove/uninstall the iPadOS Beta software before you will be able to install the Apple “officially” released version of an iPadOS upgrade/update.

Also, make sure your iPad is charged to, at least, 50%, or greater, before attempting the iPadOS upgrade/update.