Unable to set/change emoji for saved window

Steps to reproduce:

1. Create a Saved Window if one does not already exist.
2. Right-click the saved window (or select the (⋯) menu) and select Settings…
3. Set the icon to any emoji.
4. Click Save.

The icon is not updated.

Expected behavior:
The window should have the new emoji as its icon.

Orion, OS version; hardware type:
Version 0.99.123.3-beta (WebKit 615.1.16.1)
MacBook Pro (macOS Ventura 13.2.1 build 22D68)

Image/Video: