I have approximately 20 Character Inventory Slots free, but it somehow wants my Storage Space to be free.

Either when you go to buy something or after choosing the item to buy, there should be an option on where it should go. I forgot what point. The options are to go to your inventory or your storage.

EDIT: I just checked and when you first open the AC Shop screen, your cursor is at the top. By default, it should be on the option to buy something and it go to the inventory. If you press right first, it will be on the option to send it to storage. Right now, based on the text at the top of your screen, it is set to put purchases in storage.

Based on the yellow text at the top, it looks like you selected "Purchase to Storage" from the AC Shop Menu; this will send things to your default Storage box, and if that error is popping up, then that Storage is full.