Big Sur unavailable after clicking Get

If you go to the System/Software Update preference pane does it indicate that there's an upgrade (if you're coming from Catalina) available?

In either case, upgrade or update, boot into Safe Mode according to Start up your Mac in safe mode - Apple Support and try downloading from the App Store from there and install while in Safe Mode.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

Try the method from @Old Toad first. Only if that fails try

https://discussions.apple.com/thread/252713977

There are several options.

Adjustment for Wifi update - shutdown computer and move as close the Router as possible. Connect to charger. Disconnect ALL Other devices using the Wifi - want the Maximum Bandwidth for this computer.

Suggest - restart Router . Restart computer in Safe Mode - Shift - Key immediately at startup. It does a Repair Disk, clears cache files and load only Apple Software - load slowly - Normal. Once in Open Apple Apps Store and find Big Sur and download. Try not to let computer go to sleep mode or Screen Save to activate. Be patient as one knows it Big Sur is 12.18 GB size. There are often periods where it seems to pause the download , normal be patient as countdown clock may say 15 minutes but in Real Time could be 30 - 45 minutes. This can and will happen several time in the process. If all goes well. it will successfully download and attempt to Launch. Do NOT allow it to start - Quit the Installer. Check Applications Folder for new App called Install Bug Sur. Make a copy to External Drive - future usage. Now, restart again in Safe Mode - then launch the Installer.