I'm returning from a bit of inactivity, and there is a triangle with a ! in it next to my shops, and I am unable to move items into them. I saw something briefly of a new shop system, but what all am I missing?

Yep, the whole shop system was overhauled, and while your old shops (and all their contents) are still there, you must make a new one if you want to add stuff to a shop, use quick stock in general or price items now.

Detailed guide here