A basic logistics pipe without a disconnection upgrade:
https://i.imgur.com/x0QQKTH.png
The same basic logistics pipe with the disconnection upgrade installed:
https://i.imgur.com/3DWsIoQ.png

I was informed that once you apply the disconnection upgrade you have to open the pipe with the Pipe Manager to specify which sides to disconnect, but I don't see any interface for that.

Ah, I figured it out. I have to open it with the Pipe Controller. This is the kind information that would have been good to put in the guide or the tooltips.