Input method (IME) not working and taskbar icon missing on desktops created via CreateDesktop

Question

In Windows 10 and 11, the input method (IME) cannot be used on any additional desktops created via the CreateDesktop API, and the input method icon does not appear on the taskbar in those desktops.

For example, when I switch to a new desktop using the "Desktops" tool from Sysinternals Suite (which utilizes CreateDesktop), the IME becomes completely unusable, and there is no way to switch input methods from the taskbar. This issue does not occur on the original main desktop.