Hi Jan,
Can you please put this code in your bp-custom.php and see if it works as expected

////
//For Testimonials

add_filter( 'bp_testimonial_user_can_delete', 'bp_testimonial_custom_delete_permission' );

function bp_testimonial_custom_delete_permission( $can_delete ) {
	
	if ( ! current_user_can( 'publish_pages' ) ) {
		$can_delete = false;
	}
	
	return $can_delete;
	
}

add_filter( 'bp_testimonial_user_can_write', 'bp_testimonial_custom_write_permission' );

function bp_testimonial_custom_write_permission( $can_write ) {
	
	if ( ! is_user_logged_in() || bp_is_my_profile() ) {
		return $can_write;
	}
	
	$displayed_user_id = bp_displayed_user_id();
	
	$user_id = get_current_user_id();
	
	if ( ! $displayed_user_id || ! $user_id ) {
		return $can_write;
	}
	
	if( bpt_has_user_already_written( $user_id, $displayed_user_id  ) ) {
		$can_write = false;
	}
	
	return $can_write;
	//all good, get post id
	
}

function bpt_has_user_already_written( $user_id , $other_id ) {
	
	$post_id = get_user_meta( $other_id, 'associated_testimonial_page', true );
	
	if ( ! $post_id ) {
		return false;//should never happen
	}
	
	//Now check if the user has a comment on this post
	
	global $wpdb;
	
	$has_comment = $wpdb->get_var( $wpdb->prepare( "SELECT comment_ID FROM {$wpdb->comments} WHERE comment_post_ID = %d AND user_id = %d", $post_id, $user_id ) );
	
	if( $has_comment ) {
		return true;
	}
	
	return false;
}

Thank you
Brajesh

Hi Jan,
I am sorry for the delayed reply.

Please create a file in wp-content/plugins directory(If the file does not exist) and name it bp-custom.php. This file is loaded by BuddyPress before anything.

Please give it a try then and let me know how it goes.

Thank you
Brajesh

Thank you Jan.
Glad it worked.
Merry Christmas and happy holiday 🙂

Cheers
Brajesh