Hi Ramesh,
This allowed me to enable memory integrity. I then went ahead with the repair through Windows Update. After the install, the applications which were giving the COMCTL32.dll error and the side-by-side configuration error now work! However, Windows itself works less. Attempting to open Display Settings (or any settings) gives the following error alert:

Attempting to open Powershell from the right-click menu of the Windows start menu button gives this error alert:

(I am able to open powershell by searching for it, however.)
Trying to open Taskbar settings (from the taskbar's right-click menu) does nothing.
Various other built-in applications are missing, e.g. trying to open Notepad from the pin on the start menu gives the error:
ms-resource:Resources/AppDisplayName_Notepad can’t open because it can’t be found. The storage device might be missing or disconnected.
DISM and SFC run successfully now, though that hasn't fixed the above issues.
See here CBS 20250609 01.13.zip for updated CBS logs after running DISM and SFC; setupact isn't included as the file no longer exists. For some reason I was able to generate the zip without rebooting?
I rebooted after this and it didn't have any impact (besides being asked to provide a pin for my account upon login).