new product display content type not showing in products view
I finally found the problem. The answer is probably obvious for a drupal expert but not for someone who just use drupal commerce out of the box.

Right, so the search facility (search box and 'all product' link ) use the search API which needs to be re-indexed when something changed.

For some reasons it wasn't. I'm expecting that adding a new product/entiry will triggered a reindexation but it doesn't. It seems also it could be done via the cron (but I haven't set any cron either, nobody told me to so). And, anyway, it seems the indexation was 'broken' (I changed one of the category name) so I add to recreate the indexes form scratch.

So the answer is , my searches need reindexation.