Hi Ajinkya, This is Ramesh.
The KB5051987 update shows the errors 0x800f0993 and 0x80070306 on many systems. Please see if you can install it offline from the Microsoft Update catalog.
First, download the following .msu packages:
https://catalog.sf.dl.delivery.mp.microsoft.com...
https://catalog.sf.dl.delivery.mp.microsoft.com...
Save the two .msu files in a folder -- e.g., C:\Packages
Option 1: Install the .msu packages manually
First, install the prerequisite update - "windows11.0-kb5043080-x64_953449672073f8fb99badb4cc6d5d7849b9c83e8.msu"
Then, install "windows11.0-kb5051987-x64_199ed7806a74fe78e3b0ef4f2073760000f71972.msu"
Option 2: Use DISM to install the packages.
Open admin Command Prompt and run this command:
DISM /Online /Add-Package /PackagePath:c:\packages\windows11.0-kb5051987-x64_199ed7806a74fe78e3b0ef4f2073760000f71972.msu
Restart Windows.
Option 3: Repair install Windows 11 using Settings
If none of the above methods help, the best option is to reinstall Windows 11 via Settings. Your apps, settings, and files will be intact.
Please see:
Fix issues by reinstalling the current version of Windows - Microsoft Support: