Source

File: wp-includes/rest-api/endpoints/class-wp-rest-posts-controller.php

protected function check_assign_terms_permission( $request ) {
		$taxonomies = wp_list_filter( get_object_taxonomies( $this->post_type, 'objects' ), array( 'show_in_rest' => true ) );
		foreach ( $taxonomies as $taxonomy ) {
			$base = ! empty( $taxonomy->rest_base ) ? $taxonomy->rest_base : $taxonomy->name;

			if ( ! isset( $request[ $base ] ) ) {
				continue;
			}

			foreach ( $request[ $base ] as $term_id ) {
				// Invalid terms will be rejected later.
				if ( ! get_term( $term_id, $taxonomy->name ) ) {
					continue;
				}

				if ( ! current_user_can( 'assign_term', (int) $term_id ) ) {
					return false;
				}
			}
		}

		return true;
	}