Hello,
Sorry to hear you are having issues. But, I can not reproduce your issue on my Windows 11 22H2 system. The Icon stays after reboot. Refer screenshot below.

Would like to suggest try purge and reinstall steps as mention here : [Link]. Just make sure to redownload the latest version from your account page. Reboot after the purge. Reinstall and reboot again after the installation. Retest and report back here.
Thank you,
Basj,
Stardock Community Assistant.