often, problems with connecting certain Bluetooth Devices - like the PS 4 or Wii U Pro Controller - can be solved, by manually pairing it using the Bluetooth Stacks commandline tools instead of GNOME’s gui.
Run the following command:
bluetoothctl
This will open a shell where you can enter commands for the Bluetooth Stack. Enter:
agent on
scan on
Now turn on the Controller and enter pairing mode. You should see something like:
[NEW] Device 7E:4D:41:5C:B0:5D
This is the device you want to pair with. Enter:
pair 7E:4D:41:5C:B0:5D
This will pair set up the bond between your two devices. Now enter:
trust 7E:4D:41:5C:B0:5D
This will allow your controller to initiate the connection when turned on. Leave with exit. Up from this moment, the controller should also be visible in GNOME’s Bluetooth GUI.
I did everything as explained and connecting the controller with my laptop worked fine. The big picture mode of steam still does not recognize my controller though.
But, on some games i can use the controller just fine, even without big picture mode but not all games.