I think I found a solution, at least the Teams channels are no longer in my Excel and Word save dialog.
Create the following registry entries (Win-Key + R, "regedit", Enter):
[HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Explorer]
ShowCloudFilesInQuickAccess REG_DWORD 0
ShowFrequent REG_DWORD 0
ShowRecent REG_DWORD 0
ShowRecommendations REG_DWORD 0
These are equivalent to the privacy options in "Folder Options->General" in the Windows Explorer.
[HKEY_CURRENT_USER\Software\Policies\Microsoft\Office\16.0\common\privacy]
disconnectedstate REG_DWORD 2
Beware, this option disables all Add-Ins in Office applications. This option can also be set in any (recent) Office application under "File->Options->Trust Center->Trust Center Settings…->Privacy Options->Privacy Settings...", see https://learn.microsoft.com/en-us/microsoft-365-apps/privacy/manage-privacy-controls.
[HKEY_CURRENT_USER\Software\Microsoft\Office\16.0\Common\ClientTelemetry]
DisableTelemetry REG_DWORD 1
Upvote if it works for you. :-)