You need to buy a newer Yubikey with biometrics to make this work. I assume you have an older Yubikey and Google is getting to the standard by asking for a PIN.
I have a https://www.yubico.com/products/yubikey-bio-series/ and it works with Google exactly like you want it to, no PIN required. It's completely understandable to require a PIN if you don't have one of these though.
It’s no inconvenience though since the yubikey with a button to press and a yubikey with a biometric button to press work the same.
Is that how it works? A dropped house key essentially has a second factor (the address of the home), but if you have someones Yubikey that can be used for Google, is the Google Username stored in the Yubikey and accessible to the finder?
Like you can argue a dropped house key is similar to a dropped yubikey but i'd still give some benefit to the dropped house key involving real world attempts on locks with appropriate social suspicion on that if seen vs a dropped yubikey allowing anonymous attempts.
Searching online I found an answer on Stack Overflow stating that a PIN is required in this case: https://stackoverflow.com/a/79471904 How did you bypass it? I also find it idiotic that it is required. A PIN is just a password in another name, so we are back to using Yubikeys as the second factor in 2FA rather than a password replacement.