IPhone earbuds with iPad Pro

Not out-of-the-box. There are 3rd party adapters that allow this to work. Belkin, for example, makes a USB-C to Lightning Audio adapter that would work with your current EarPods. You can also get a USB-C to audio adapter (this would let you use any headphones that have an audio jack -- but not your current EarPods).

The iPhone 7 came with "EarPods with Lightning Connector"

If you check the Apple website on compatibility (for the EarPods), you'll see:

Works with all devices that have a Lightning connector and support iOS 10 or later, including iPod touch, iPad, and iPhone.

The iPad Pro 2nd Generation comes with a USB-C port - it will not work.

Apple provides an excellent document to help you identify the ports on your Mac: https://support.apple.com/HT201736. While it doesn't specifically mention iPads/iPhones/etc. it can help you clarify the "lingo" that can get confusing.