My luggage was TAG thru on a EDI-LHR-AMS-HKG booking with an overnight transit at LHR.

Yet my luggage info is not in CX system (BA agent at EDI has reminded me to double check with CX at AMS) when i talk with CX agent at AMS.

Tag through is usually not problematic - they dont even need your PNR. I have once a KUL-MNL-HKG on MH and CX, MH just need to know which flight i m taking at MNL-HKG, not even the booking or ticket itself. Instead it is more important to check at transit that CX got the baggage tag number.