Account Recovery

Your profile shows you are running macOS 10.15. You need to be running macOS Monterey to set up a recovery contact. From the article posted above.

Requirements for setting up a recovery contact

• All of your devices must be running iOS 15, iPadOS 15, watchOS 8, or macOS Monterey or later. You might be prompted to update any devices not running the latest OS, or remove any devices that you aren't using.
• You must be over the age of 13.
• You need two-factor authentication turned on for your Apple ID.

See this link and follow the instructions provided to set up a recovery contact

Set up an account recovery contact - Apple Support