You can view how many bone shards, paintings and runes you've found when you are done with your mission. Can I view how much of the items I've already found while doing the mission?
You can't see it in the menu or anywhere else. The only things you see is:
But you can take a look at a list of collectables per level to get the info early enough and just remember how much you already found in a specific level. Such a list can be found here.