The fix of the issue is now available in the latest InDesign 2022(v18.104.22.168). We recommend you upgrade to the latest version for the fix.
If you are unable to see the update, go to the Creative Cloud application and click on the context menu on the top right and click on Check for App Updates.
Adobe InDesign Team
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Having a warning dialog appear to inform a user that the document is already open by another user is a very important part of any workflow where multiple users access the same file. The "read only" status of such a file is subtle and easily missed. Please Adobe add a warning dialog for this situation!