you require permissions from TrustedInstaller to make changes to this

I have recently formatted my system. I had copied the items of C:\Windows\WinSxS from my previous install in a USB drive and then formatted the laptop. Then re installed windows and copied the contents of USB drive back to C:\Windows\WinSxS
however I notice the boot time has again become long as it was previously. So I decided to delete all the items in WinSxS folder. I get a few errors like the one in screenshot.

I am not able to resolve this error.
What should I do to get rid of this Trusted Installer permission error. I want to delete every thing from WinSxS folder.

After reinstalling windows ... why did you restore the saved contents of WinSxS?
And then, having done so, why do you want to delete everything from that folder?

Is there a reason you've not simply performed a clean install?

After a clean install it worked fine, I thought it will keep downloading updates from internet. Some where I had read that it stores things in WinSxS folder. So that it can roll back to previous state. So I had copy pasted the contents of previous install so that it does not download 12 GB again. In previous installation the size of this folder had grown to some where 12 Gb . So to reduce internet band width wastage I did so. However after a reboot the system became a bit slow. Meaning it takes long time to boot to desktop screen. So I decided to delete the contents. I recently read this
one How to Get Permission from TrustedInstaller in Windows 10/7 so I am trying things from here now.

The changes I have made can be seen here

The option to select principal seems greyed out to be able to give full permissions to Administrator

I am now getting this error.
But now in some sub folders and files of WinSxS I get this error.

Seems I have missed something. What exactly is that I am not clear.

- - - Updated - - -

Some one suggested me to use dism and not to manually touch the WinSxS folder as deleing it may leave computer unusable. So I did this

1) dism /online /Cleanup-Image /AnalyzeComponentStore

Code:

C:\Windows\system32>dism /online /Cleanup-Image /AnalyzeComponentStore
Deployment Image Servicing and Management tool
Version: 10.0.19041.844
Image Version: 10.0.19041.1110
[===========================99.1%========================= ]
Component Store (WinSxS) information:
Windows Explorer Reported Size of Component Store : 10.74 GB
Actual Size of Component Store : 10.41 GB
    Shared with Windows : 5.52 GB
    Backups and Disabled Features : 4.89 GB
    Cache and Temporary Data :  0 bytes
Date of Last Cleanup : 2021-08-02 11:58:47
Number of Reclaimable Packages : 1
Component Store Cleanup Recommended : Yes
The operation completed successfully.

2) dism /online /Cleanup-Image /StartComponentCleanup

and this resulted in 6.5 Gb of WinSxS folder

I want to reduce its size further if it is possible.

WinSxS is a system folder in Windows. That’s why it’s located on the system partition. WinSxS stands for “Windows Side by Side,” which is a good description of the folder’s purpose: different versions of files are stored together, side by side. The folder is also called the component store. It primarily contains system files and can be several gigabytes in size.

sandila said:

I want to reduce its size further if it is possible.

I am a disk-space zealot, but even I shy away from messing with WinXsX most of the time. It does grow, and MS offers no helpful advice on how to slim it down (that I know of), bar 'remove unwanted software'. But nothing will tell you which bits of sw are responsible for any WinSxS bloat. I do recall that, back in the Vista days, I had 6 versions of 'Microsoft natural language search', at ~300MB each - and those got the order of the boot. The DISM commands you mention are supposed to help, but they never make much difference on my PC, which is currently 109,000 items, and 6.6GB. But a lot of that is links, and (according to Wiztree), only 2.2Gb of disc space is used.

Here is your mistake ...

sandila said:

I want to reduce its size further if it is possible.

Disk space is too cheap to conserve. Your time spent cleaning things is more valuable than the cost of storage.

If you're slimming things down because your drive is too small, buy a bigger drive. They're cheap. Really cheap.