This was an important piece of information shared in the Live Letter and it would be good to get the word out in advance.
We cannot use Island Sanctuary as a place to store outdoor furnishings that we're currently keeping in inventory or on retainers. How furnishings work in Island Sanctuary will be different from how they work in housing. It is somewhat based on the glamour system. My understanding of how it will work is a bit shaky since all I have to rely on is the subreddit translation by Miuna but here goes best that I can.
When we want to add furnishings to our Hideaway (the area where they can be placed will be marked in blue when the furnishing interface is open), we will apply an Island Prism to the item in our normal inventory. That will generate a copy of the item (that they seem to be calling a mirage?). If you want to use multiple of that item, you can apply multiple prisms to the same item to create multiple copies. You won't need multiples of the item in your inventory. The original item stays in your inventory and is not consumed so you could take an item currently placed at your house, copy it in Island Sanctuary then put it back at your house.
The furnishing interface will have a list of furnishings saved and furnishings placed. Once a furnishing has been saved to the list, you will not need to have it in your inventory to place it again. I could not tell from the translation if an Island Prism will be needed every time you want to place another item or only to save it to the list though I think it's needed to place.
The controls have the standard placement (still no Z axis) and rotation. Instead of the return to inventory bag or storeroom options, there's a single option to remove the furnishing (dispel the mirage?).
If anyone is able to give a clearer explanation of the process from another translation or source, feel free to add it. Someone in the chat during the stream did express disappointment that we won't be able to store the actual furnishings on the island and YoshiP said it wasn't something they had in mind when working on the system
Regarding Island Prisms: they're going to increase the number of prisms yielded when crafting at some point in the future but it was unclear if they meant in 6.4 or a later date. Crafters may want to gather the needed materials in advance but wait to craft them until the patch (you won't be any worse off if the increase is delayed). It's hard to say what's going to happen to prices on the marketboard for those who are not crafters so you'll have to take your chances on buying now or waiting until later.