For more information on the Illusions system, see Grim Misadventure #112: A New You; but yes, the illusions/wardrobe options are available to all characters.
Here’s a clip from a stream Zantai did showing the Illusions, https://youtu.be/Jx1WM6YgLPw?t=1h18m49s.
The devs are expanding the storage available, but it won’t be unlimited.
Edit: Here’s where Zantai shows off the stash in that same video: https://youtu.be/Jx1WM6YgLPw?t=1h3m3s.