When opening your processing window (L), your inventory also opens. If you then click on the Artifact Inventory button, both the processing window and inventory window close and the artifact inventory doesn't appear.
The artifact inventory is great for longterm storage of unused artifacts and lightstones. But for those items we use regularly, e.g. switching between sets for various lifeskills or combat activities, the Artifact Inventory makes things much worse.
If you have the inventory space spare I would recommend not touching this update for daily-used artifact sets, It is a reduction in quality of life for us. At least not until it's improved. As of right now all it's done is necessitated an additional window that we need to open, and move artifacts to and from. It's literally doubled our mouse clicks and time it takes to change artifact sets.