You don't need, and can't use a recovery key if you are using two-factor authentication. On recovery keys, see Two-step verification for Apple IDhttps://support.apple.com/en-us/HT204152.
Are you in recovery under two-factor authentication. If yes, see Recover your Apple ID when you can’t reset your password https://support.apple.com/en-us/HT204921which you may need to use.
Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your identity. After you request account recovery, you'll get an email with a confirmation of your request and the date and time of when you can expect to regain access. … When the wait period is over, Apple sends you a text or automated phone call with instructions to regain access to your account. Follow the instructions in the above link to immediately regain access to your Apple ID.
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But, also see this document (maybe it is where you became curious about recovery keys): If your Apple ID is locked or disabled https://support.apple.com/en-us/HT204106 "If you or someone else enters your password, security questions, or other account information incorrectly too many times, your Apple ID automatically locks to protect your security and you can't sign in to any Apple services.
If you use two-factor authentication, you need a trusted device or trusted phone number to reset your Apple ID password and unlock your account. If you have a recovery key, you can also use it to help you regain access to your account. …
If you use security questions with your Apple ID, or if you don't have access to a trusted device or phone number, go to iforgot.apple.com. Then you can unlock your account with your existing password or reset your password. After multiple unsuccessful attempts to unlock your account, your Apple ID will remain locked and you can try again the next day.” Eventually you very likely will end up in account recovery.
Apple support might be able to help you if you have your receipt for the purchase of your device from an authorized Apple seller with its serial number on it. See the support options below. Alternatively, if an Apple Store is open in your area, then you can go there to deal with your problem. In this case, you can make a genius-bar appointment (https://www.apple.com/retail/geniusbar/) if you want.
Get Support: We’re here to help https://getsupport.apple.com/. Go through the options to find the best support option.
Apple Support Twitter https://twitter.com/AppleSupport
Apple ID account security for country-specific and region-specific help https://support.apple.com/en-us/HT204169