Thank you all for explaining.

The behaviour I was expecting was to click ‘login’ on the feddit.nl page, and that login page to recognise that I was logging in with the credentials used by lemmy.ml, and to log me into lemmy.ml instead, and then to be redirected to the ‘local’ version of the link on the lemmy.ml instance.

Rather than it just be a feddit.nl login page only, and be told ‘log in not recognised’. That’s where my confusion came from. I’m like “wait, I can’t log into Lemmy here? why?!”