Email OTP login using "verify_email_by_code" template instead of "auth_email_by_code"

While testing the login flow in my application, I noticed my custom template for auth_email_by_code (Authentication Email (Code)) was not being used during login after sending the code. Instead, verify_email_by_code (Verification Email (Code)) was being used. I was able to confirm this by using my custom template for verify_email_by_code (Verification Email (Code)).

“Email OTP for login” was active and both templates were enabled.

Am I misunderstanding the usage of these templates, or is there a misconfiguration somewhere?

Any answers are greatly appreciated!