Not sure if I've got the right end of the stick here and don't know your new procedures.
Over here in Oz , our duty of care outside of controlled airspace extends to giving traffic if WORK LOAD permits. it is also communicated if the level is unverified and paint is unidentified, (if we have not been in contact and not verifed the aircraft)also if aircraft seems to be climbing , descending or currently maintaining
We can also SUGGEST a turn to avoid confliction. but we say e.g." Suggest turn right 30 degrees ". This leaves the PIC in no doubt that they are being given the best info TO OUR KNOWLEDGE and that they are being given an option for their self separation, but the decision is up to them.
Hope this helps.
We have also had the situation where an aircraft had his control services terminated, left controlled airspace, diverted from his planned track and sometime later was a CFIT.
The controller got alarms that the aircraft had flown off track outside controlled airspace, there was a push from outside motor mouths that the controller had a duty of care to advise the pilot that he was deviating from his track, even though control services had been terminated. Try
200402797 this is the report.