Another way to mitigate this issue is to store a secret in the browser that initiated the link-request (Ex. local storage). However, this can easily break in situations like private mode, where a new tab/window is opened without access to the same session storage.
An alternative to the in-browser-secret, is doing a browser fingerprint match. If the browser that opens the link doesn't match the fingerprint of the browser that requested the link, then fail authentication. This also has pitfalls.
Unfortunately, if your threat model requires blocking bots that click too, your likely stuck adding some semblance of a second factor (pin/password, bio metric, hardware key, etc.).
In any case, when using link-only authentication, best to at least put sensitive user operations (payments, PII, etc.) behind a second factor at the time of operation.
