Bank space ??
You have to buy the bank space in the bank tab with gems. I don’t recall how many gems it costs though.
“Have fun storming the castle.”
600 gems. But unless your cooking I find I didn’t need it. You can combine un-wated Dyes at the mystic forge and store crafting materials in the collection tab. That frees up much space!
I was confused at first too. It’s not in the gem store, it’s in the bank interface itself. If you look under the tab you already have, all the way to the right, there is a lock icon. Click on that (maybe double click, not sure), and you will be given a choice to buy another tab.
Extra bag slots is the same way- it’s in the inventory interface.