found the solution: simply needed to remove the double quotes around the value
// The product's related artist.
$artist = get_field('artist_id');
// The product's most recent related project. If found, get the content of its "Artist" block.
$project = new WP_Query( array(
'post_type' => 'project',
'posts_per_page' => 1,
'order' => 'DESC',
'meta_query' => array(
'key' => 'artist', // name of custom field
'value' => $artist->term_id,
'compare' => 'LIKE'
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