Macbook Pro 11,3 No longer has a serial number THE ISSUE:
Mac OS No longer has a serial number and shows &quot;Serial Number (system): Not Available&quot; in system profiler.
STEPS TO PRODUCE THE PROBLEM:

I had a botched filesystem runnig mac os Catalina 10.5.7, and so i decided to do a clean  install, and then do an internet recovery. To be sure my ssd was totally clean including the efi partition, i zero'ed the drive with dd. Then, booted to internet recovery, which oddly booted up to Big Sur recovery even though i never upgraded to Big Sur. I decided to install Big Sur anyway via internet recovery, and after the install, i noticed that in &quot;About this mac&quot; as well as through a terminal command, that my serial number was labeled as &quot;unavailable&quot;, and is no longer recognized in the MLB of the &quot;Mail logic board.&quot;
Furthermore, i noticed that my icloud automatically signed my mac out from my icloud interface in the settings panel on my iphone. I never signed myself out before erasing.

EXPERIMENTS AND QUIRKS:
One more strange quirk is that apparantly, this somehow also deactivated all of apples DRM (digital rights management) for any of the apps that i had purchased. I concluded this, because after the clean install from internet recovery, I DID NOT SIGN INTO ICLOUD. Then, instead of importing my files with migration utility, i simply dragged and dropped my digitally purchased app store apps from my time-machine backup, onto my clean install. After removing time machine drive, i opened the apps, and low and behold, all of them worked perfectly without asking me to sign into icloud, or log into the app store. How is this possible?
MY IDEAS PERTAINING TO THE ISSUE:

Supposedly, once a certified apple technician burns a serial number into your logic board, it is impossible to remove unless you have specialized software that contacts apples servers with a registered signature and encryption key, and waits for apples servers to send authorization to write or remove the serial number from the logic board. Assuming that apples technology is impenetrable, then you would have to assume that someone stole apples special software and one of their keys, and used it on my logic board remotely to deserialize my mlb.

The other possibility, is that apples hardware and logic boards are flawed, and they can erase their oen serial numbers. other than that, im out of ideas.


MY QUESTION:

Can someone explain how i lost my serial number, and explain the weird quirks (missing drm, unauthorized deregistering my mac from icloud) that are happening as a consequnce?

Then, can someone please tell me how I can get my serial number burned back into the mlb so that i can use imessage on my mac again?

I found a website with some software called BlankBoard Serialzer at https://www.macintoshrepository.org/26584-blank-board-serializer?ns=1
Could anyone tell me if this sofware is safe to use and if I should use it to re-burn my serial number into my mac?


Thanks for any help! Check screenshots below!
Question 1a:
We don't know all the steps you have taken (and you may not remember all of them very clearly) in your reinstall.  So hard to say why.  The most common causes are some hardware change, but you say this does not apply in your case.  Of the steps you mention using dd is the only unusual step - I would have used Disk Utility in Internet Recovery.
Question 1b:
You have already discovered that some Apple services require a valid serial number. iMessage and various DRM are tied to your serial number and UUID as well as Apple ID.  As an aside, loading a valid serial number is a tricky and important step in getting a Hackintosh to run iMessage.
Question 2:
The best solution is to take the MBP to an Apple Store where they may well fix your problem for free - just say it happened during a macOS upgrade (which is true in your case).
Question 3:
The Blank Board Serializer is an Apple tool and can be used to fix your Serial Number.  It is important to find the version which is compatible with your MBP - I can't help you there.
Have a read of these three links which describe the process which must be following very carefully - the first one has lots of comments from those who have succeeded (or not) using this method.
Roger Sen
What causes Mac to lose its serial number
How to fix missing serial number
Warnings:

However you fix this (either via Apple or yourself) make very sure you enter the correct serial number belonging to your Mac.  You only get one chance to get it right.
If you do it yourself, be prepared that you might get it wrong and brick your MBP.

Additional warning:

Read @DanRan's own solution and heed the warnings about the need to unregister the Mac and unauthorise from any services which have been used with the incorrect or blank serial number.