See the thread that I started two days ago:
Using YubiKey Security Keys with iOS 16.3 beta It's currently only five threads down from yours.
YubiKey NFC works fine on an iPhone. However, note that iPads, at least the ones without cellular, do not have NFC functionality. The Yubico site has a page about using a YubiKey with an iPad.
The YubiKey model that you're considering has a USB-A connection. Another option is to use a USB-A to Lightning adapter.
If you're using Google's Authenticator app or similar, I would suggest changing to Youbico's own Authenticator app, which will work on your computer as well as on your iPhone. There's a photo of Yubico's app in post #8 of the thread that I started.
EDIT: As you'll see from the thread that I started, there may or may not be an issue with my YubiKeys on login to my iPhone. Reading your post, it's occurred to me that I should try plugging a YubiKey directly into my iPhone at login, just to see what happens. Unfortunately, I don't have a USB to Lightning adapter handy at the moment. That
possible issue aside, NFC is working fine with the phone.