Well, it happened again and the result can be seen at the beginning of the stream on https://www.twitch.tv/videos/671571185

The following are the steps that happened:
0:00:00 I say 'hello' to my Free Company (with the keyboard)
0:00:12 I open the 'Party Finder' window (I normally set it to look for Hunt only) via the short-cut I put on my hotbar
I try to move the cursor with the up and down on the d-pad of the controller and as you see it doesn't work. Somtimes the cursor appears for a short time, but it will not move to the menu or any other entry.
0:00:39 I pull out the dongle that connects my wireless keyboard to the PS4, so now only the standard Sony DS4 is connected. (The big scrambled block on the left covers the keyboard disconnect message, which is standard PS4 streaming behaviour to cover sensitive information like user-id)
I continue to try moving the cursor with only the DS4 connected, with absolutely zero success.
0:01:15 As I have show that the problem persists when only the DS4 is connected, I reconnect the keyboard dongle. (the big scrambled block on the left covers the keyboard connect message)
Continuing to try to move the cursor is still unsuccessful.
0:01:26 I use the ESC key on the keyboard to cancel the Party Finder window
0:01:29 You can see the cursor is not showing as normal in the main menu too.
0:01:25 I open the HUD Layout and move the inventory grid with the mouse-pad on the keyboard a little
0:02:06 I cancel the HUD Layout by using the mouse-pad and mouse-buttons on the keyboard
0:02:20 The mouse cursor now works normally in the main menu again (via the d-pad of the DS4)
0:02:32 And also the mouse cursor works normally again in the Party Finder window (via the d-pad of the DS4)

I hope this shows you enough information to have any clue what the problem is here.
This problem occurs very rarely (this is the first time since the previous report from above).