On your code, the function wp_get_post_terms() return an array of WP_Term objects, so you can’t access directly to an object property without specifying an index for the array like :
$terms[0]->slug
Otherwise, you should iterate through the whole array of terms and retrieve the slug into an another array, like :
$terms = wp_get_post_terms( $post_id, 'disciplines' );
$terms_slug = [];
foreach ($terms as $term) {
$terms_slug[] = $term->slug;
}
And finally, you can implode the all the gathered slugs into your class attribute :
class="filter-item <?= implode(' ', $terms_slug); ?>"
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