TotalSegmentator: Failed to install required packages (win10)

Thanks, this additional information helps a lot. It is likely that your institution interferes with your internet access.

You can find several similar topics, see for example [1] and [2].

Probably the simplest solution is to install Slicer and extensions on a computer with proper internet access and then copy that Slicer to the computers where you need to use it. Slicer is fully portable, so if you only copy the Slicer installation folder and downloaded TotalSegmentator weights from your user folder then it should all work.