Since recent update, iPad keeps saying “verifying 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

If you continue to experience difficulties with direct update from iPad Settings, you may have more success if you perform the update using a PC or Mac computer. To do so you will need access to either a PC (with iTunes 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.

Have you successfully updated to iPadOS 15.1 - or are you instead attempting to perform this update?