how do i know if i have a recovery key set up

... because you would have been offered a randomly generated 28-character code (key) that you were supposed to store in a safe location should you need it.

Ref:

• How to generate a recovery key - Apple Support

If you lost your Recovery Key

As long as you remember your Apple ID password and still have access to one of your trusted devices, you can sign in and create a new Recovery Key.

1. Go to your Apple ID account page.
2. Sign in with your password and trusted device.
3. In the Security section, click Edit > Replace Lost Key.

Keep your new Recovery Key in a safe place. Your old Recovery Key won't work anymore and you can't use it to reset your password or access your account.