I can confirm after installing Windows 11 update KB5013943, the Corsair Service would fail to start.
Uninstalled ICUE, cleaned folders and system of any ICUE leftovers, Rebooted and Re-Installed ICUE_4.23.137 and on reaching 77% the install hung for a minute and then ICUE popped up "Corsair Service failed".
Tried to install ICUE with Administration privileges (as I installed Windows 11 on a local account instead of signing in to a Microsoft account, due to their excessive Data Collection practices these days with Windows 11),... Anyway, moving on, right clicking on the iCUESetup_4.23.137 would not show any options to install with Administration privileges though these options do show up on other installers, Just not on ICUE.
Anyway, no luck with getting Corsair ICUE to work on Windows 11 after installing KB5013943,... So I came here and tried Ali-S approach and this worked for me after Uninstalling KB5013943.
I think I'll wait for a Corsair or Microsoft fix.
Thanks Ali-S