Per Yubico’s specs on the Yubikey 4, it does not support FIDO 2 resident credentials, meaning it does not support Passkeys.

Compare to the specs of the Yubikey 5C NFC or Yubico Security Key C NFC, which both have this section:

FIDO2

The FIDO2 application allows for secure single and multi-factor authentication, and can store up to 25 resident credentials. These credentials, which are protected by a PIN, enable passwordless login, where the YubiKey, unlocked by a PIN and authorized by touch, can log you in to your accounts without entering a username or password. The FIDO2 application is FIDO certified.

See also Yubico blog post with an FAQ about passkeys:

How are passkeys different from YubiKeys?

They’re the same, and they’re different.

They’re the same because YubiKeys have had the ability to create these passwordless enabled FIDO2 credentials (passkeys) since the YubiKey 5 Series became available in mid-2018. Currently, YubiKeys can store a maximum of 25 passkeys. We are evaluating increasing this in the future because of the likely increase in fully passwordless experiences across the web that require them.

They’re different because Platform created passkeys will be copyable by default using the credentials for the underlying cloud account (plus maybe an additional password manager sync passphrase), whereas passkeys in YubiKeys are bound to the YubiKey’s physical hardware where they can’t be copied.

I wouldn’t run out right now and buy a Yubikey to store Passkeys given the 25 key limit and the likelihood that Yubico releases a new key that supports storing far more of them, but if you do, the $25 Security Key series is the cheapest option.