Microsoft has now expanded the availability of Windows 10 version 21H1 aka the May 2021 update. The update is now available for all users with their Windows 10 PCs running versions 20H2 and 2004, if they manually check for updates.

Microsoft has also started to automatically update devices on Windows 10 version 2004 to 21H1 in the first phase of what it calls the “Machine learning” training. It will however do so in multiple phases.

Current status as of June 2, 2021
Windows 10, version 21H1 is available for users with devices running Windows 10, version 20H2 and version 2004 who manually select “Check for updates” via Windows Update. The recommended servicing status is Semi-Annual Channel.
We also started the first phase in our rollout for machine learning (ML) training, targeting devices on Windows 10, version 2004 to update automatically to Windows 10, version 21H1. We will continue to train our machine learning through all phases to intelligently rollout new versions of Windows 10 and deliver a smooth update experience.
Note We are initially throttling up availability over the coming weeks to ensure a reliable download experience. As a result, the update may not be offered to you right away. For more details, see How to get the Windows 10 May 2021 Update.
So, in case you are currently running Windows 10 version 2004 and 20H2 and want to update to 21H1, you can do so in many ways. Click here to learn more about updating to Windows 10 version 21H1.