When I tap and hold on an empty area on the homescreen, nothing happens. No plus button shows up.

You can learn about adding Widgets to both your Home Screen - and Today view - here:

> Add widgets on iPad – Apple Support

> Use widgets on your iPad - Apple Support

Ensure that you have updated your iPad to the most recent version of iPadOS - currently iPadOS 15.4.1. 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 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.

Widgets are available using iPadOS 15 or later. You might need to update your unidentified iPad model.

Regards

Giulio