Windows 11 trying to sneak onto Windows 10 system?

How do I update to Windows 10 21H2 without Windows 11 sneaking in?

When notified that your device is compatible with Windows 11, simply choose the option, to stay on Windows 10. At this point, you will have to manually elect to upgrade to Windows 11.

How would you go about it?

When prompted to upgrade to Windows 11 decline the upgrade. It’s unnecessary to disable TPM support to block Windows 11. At this time Windows 11 is still an optional upgrade and Windows 10 is fully supported until 2025 so there is no reason that will change.

If you really want to make it impossible for Windows 11 to be installed. You can configure the Select the target Feature Update version group policy to 21H2. The first field should be set to Windows 10 while the second field should be set to 21H2. This policy will prevent Windows Update from installing Windows 11.

Registry Key:

Windows Registry Editor Version 5.00

[HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Microsoft\Windows\WindowsUpdate]
"ProductVersion"="Windows 10"
"TargetReleaseVersion"=dword:00000001
"TargetReleaseVersionInfo"="21H2"

I have used Windows Update to upgrade to Windows 10 21H2, and Windows 11 didn't sneak in.

If Windows Update proposes "Feature update to Windows 10, version 21H2", then you are good to go.

If it doesn't, you may still download directly the upgrade from Microsoft's page of Download Windows 10, where you can choose between doing the upgrade from there, or to create a Windows 10 installation media and use it instead.