iPhone password reset without recovery key

You can’t. Once you set up a recovery key you take complete responsibility for the security of your account; Apple can no longer access your account, and Apple employees cannot reset it for you. This was explained when you created the recovery key, and you were told to keep it in a safe place→Set up a recovery key for your Apple Account - Apple Support. If you have other trusted devices on your Apple Account you can use them as a way to reset your password.

From the link:

A recovery key is a secret 28-character code that you can use, along with a trusted phone number and an Apple device, to recover your account and data.

• When you set up a recovery key, you turn off Apple’s standard account recovery process.
• Instead, access to a trusted device or your recovery key will be required to reset your Apple Account password and sign in to your account if you ever lose access.

This gives you more control of your account recovery methods and can help prevent an attacker from gaining access to and taking control of your account. However, if you lose your recovery key and can’t access one of your trusted devices, you’ll be locked out of your account permanently.