[Bug] ITL: Rewrite causes focus issues on window removal

[serebit]

Description

The newly merged rewrite of the ITL causes a reproducible (at least on my machine) issue with window focus. Applications can get into a state where they cannot be focused via the applet, but can be focused by clicking on their window. The inability to focus is cleared upon clicking on the window directly.

Budgie version

budgie-desktop 10.9.1 (git-ebec0912c0f6db5f8f3c2f1baa6f6d1f67a1cf20)

Operating System

Arch Linux

Steps to reproduce the issue

1. Open multiple applications, including one Firefox window
2. Open an additional Firefox window
3. Select a non-Firefox window, then re-select the newly created Firefox window (this sets the non-Firefox window as the next most recent)
4. Close the newly created Firefox window via its menubar Close button (the non-Firefox window should now be focused)
5. Attempt to focus on the remaining Firefox window via the applet

Actual result

budgie-itl-bug-2024-04-22_10.58.03.mp4

Expected result

On Firefox window removal, Firefox should be focusable via the applet.

Additional information

No response