Thank you - as sibling also mentioned, what you're describing in isn't a magic link but a standard TOTP/HOTP delivered via email which absolutely is phishable in the manner you described.

Magic link is a process where you enter your email address and the service sends you an email that contains a clickable hyperlink that contains a cryptographically strong, short-lived nonce in the URI that is used as a proof-of-possession factor (the email account) to authenticate users.