After a fresh night of sleep, I think I finally got it!
I did notice I had a typo (should be $term->term_id) in the example above, but I only wrote that as an example so it wasn’t the actual code that I ran.
Regardless, it was really simple once I found out about “Display a value from a specific post“. I didn’t expect it working for terms as well so I disregarded it at first.
<?php
$terms = get_field('multiselect_movies');
if( $terms ): ?>
<?php foreach( $terms as $term ): ?>
<?php
$term_id = $term->term_id;
$movie_id = "movie_" . $term_id;
the_field('movie_website', $movie_id);
?>
<?php endforeach; ?>
<?php endif; ?>
