After some trial & error, re-installing the entire A350 i figured out the issue and it was a setting within Simbrief - so nothing wrong with the moduel itself (which kind of makes sense since the uplink for the EFB works just fine).
Within the Simbrief planning tool you have to enable the "Detailed Navlog" setting otherwise it won't be able to import anything into the FMS!
If you scroll further down to the dropdown "Flight Plan Downloads" it will tell you exactly that.