@Guillaume LOYER, Thanks for posting in Q&A. Yes, your understanding is correct. each publisher is responsible for the versions of its application on the different stores. And it seems the Slack app is not updated in Microsoft Store new. This needs Slack support to upload the new update in Microsoft Store new. I notice you have opened a ticket to Slack. You can ask them to do this.
Meanwhile, apps that are deployed from the Microsoft Store new are automatically kept up to date to the latest version of the app. For this feature to work properly for UWP apps, the Turn off Automatic Download and Install of updates should not be enabled. So if the new version update is published, the device will automatically install it.
https://learn.microsoft.com/en-us/mem/intune/apps/store-apps-microsoft#app-update
Hope the above information can help.
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