JSLIM 

You were almost there (managing it from SPO\OD4B) as Teams are relying on those service for 1:1 chat and Teams Channel file sharing.

One of the thing you can consider are:

• Control who can create Teams and Channel or lay a process where in only select Help desk can create Teams\Channel
  • https://docs.microsoft.com/en-us/microsoft-365/admin/create-groups/manage-creation-of-groups?view=o365-worldwide
• By then the help desk can facilitate request by adding granular settings below

  • Block Download or Offline Availability in SPO\OD4B

     

    File Level

     

    • https://techcommunity.microsoft.com/t5/microsoft-onedrive-blog/onedrive-message-center-update-november-1st-to-november-31st/ba-p/288957

     

    Site Level for  SPO\OD4B

     

    • https://support.microsoft.com/en-us/office/prevent-users-from-downloading-content-from-a-site-98821ec7-cc99-4393-a002-f73370ba6694 (Site Collection - SPO)
    • https://answers.microsoft.com/en-us/msoffice/forum/all/use-onedrive-for-business-in-online-mode-only/36445916-c281-4d5c-8f0f-4a0e0916eafb (Personal Site - OD4B)
    • Additional instruction to access Library Settings: OneDrive Site > Return to Classic OneDrive (Lower Left) > Click the Gear icon > Show Ribbons

     

    Client Level (Restrict Sync using NGSC)

     

    • https://docs.microsoft.com/en-us/onedrive/allow-syncing-only-on-specific-domains (best for Local Workgroup or non-domain joined machine)

There's some loophole on this that I can't recall as of the moment or maybe part of them are not applicable but feel free to mention me back in case.

Also some promising note here:

https://onedrive.uservoice.com/forums/913531-onedrive-sharing-collaboration/suggestions/7105024-prevent-shared-files-from-being-downloaded

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Note: I do this on my free time to help foster the cloud community. Please also mark my response accordingly.

BFN