The short answer is that DS4 behaves differently over Bluetooth than over USB. To get it working on Windows, use a third-party driver that makes DS4 inputs accessible through the XInput API. You can use Steam for this by enabling PlayStation Configuration Support and running the game with the Steam overlay. DS4Windows is another option.
The technical explanation is that DS4 can operate in two modes while connected over Bluetooth. DS4 defaults into a PC-friendly mode that provides button, thumbstick, and trigger inputs but excludes other features like the touchpad, gyroscope, and accelerometer. (Probably this is done to save battery.) The PC-friendly mode doesn't support vibration or changing the color of the light bar. To access the other features, a report must be sent to the controller to tell it to switch modes. Once it's in the full-feature mode, it stops sending the PC-friendly inputs. For more info, see DS4-BT on psdevwiki. Input report 0x01 is the PC-friendly report, input report 0x11 is the full-feature report.
My guess is Fallen Order either doesn't support DS4 over Bluetooth, or it only supports the PC-friendly mode. If you use your DS4 with Steam, it will already be initialized into the full-feature mode. Try closing Steam and turning the DS4 off and on again.