@Caspar - ABO, Thanks for posting in Q&A.
To clarify this issue, please do some checks below.
1.Sync and Restart the device to check whether teams can install successfully.
2.Check if there exist some error message in Event Viewer.
3.Deploy Teams desperately: You can download the Teams installation package in official website and upload it to Intune, then you can deploy it as Win32 app.
https://learn.microsoft.com/en-us/mem/intune/apps/apps-win32-add
Please try above information, if there is any update, feel free to let me know.
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