I’ve just erased my mac through disk utility so I can install the mac update (after i have tried all the options on Apple website)

Make sure that you are connected to the internet, preferably with a wired Ethernet connection. Then restart your Mac in the Internet Recovery Mode pressing the Option + Command + R keys to download and install the latest OS that is compatible with your Mac.

What Exactly happens when you choose " Reinstall macOS Big Sur " from your image above

Just below " Restore from Time Machine " and above " Safari "

This is all predicated on the computer has a functioning Internet Connection

Otherwise, you will be a Error Message about No Internet Connection or perhaps some error code that makes not sense to normal people like you and me

Not at this moment. Please tell us what happened when you "tried this"? Without knowing more specifics, it's not possible to do much more than guess.

Use Disk Utility to erase a Mac with Apple SILICON

Then have a few suggestions ;

1 - Get Support Choose a product and we’ll find you the best solution.Start now and open an Apple Support Ticket as they are Apple Employees to deal will these types of issues . 

2 - Have the computer evaluated by the Professionals who have the Special Hardware Software and Expertise to diagnose the issue and offer possible solutions

3 - Make an Appointment at the Apple Genius Bar or call 1 800 MyApple and have them evaluate the computer

4 - Contact Apple for support and service

Then, physically take the computer to an Apple Store or Apple Authorized Service Centre as previously suggested

They have the Special Hardware Software and Expertise to diagnose the issue and offer possible solutions

If an error occurred while updating or installing macOS

Use Disk Utility to erase an Intel-based Mac

Free up storage space

How to repair a Mac disk with Disk Utility

Intel computer ?

Apple Silicon Computer ?

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