Your site makes me make an account before I can use it, whereas excalidraw.com doesn't, and also excalidraw.com seems to save my drawing just fine? I closed a tab and reopened it and my drawing was still there, presumably from localStorage.
The three-lines-menu also has a "Save to..." option that lets you create a sharable link or save to your local disk.
The three-lines-menu also has a "Save to..." option that lets you create a sharable link or save to your local disk.