To know which email you’ve linked to your account, go to Profile > More > Account.
If you’ve signed up with your Apple ID, your email found here likely ends with @privatrelay.appleid.com—it’s the address generated by Apple when you decided to sign up with your Apple ID. This means that whenever you need to log in to Sleep Cycle, you’ll select "Log in With Apple" and follow the instructions.
If you’ve signed in with Google, the method is the same - you select "Login With Google"
If you wish to change the email associated with your account, check out this article:
https://support.sleepcycle.com/hc/en-us/articles/14757315058460-Updating-Your-Account-Email-Address